Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations

::Needs to be reviewed: 2. Paul August ☎ 20:04, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6170 \Psi is surjective if and only if \Psi^\ast is injective], id=6170 -- WP guess: \Psi is surjective if and only if \Psi^\ast is injective -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=484 biconditional], id=484 -- WP: logical biconditional -- Status: M

:: Copied the section "Colloquial Usage" from PM into WP article. Paul August ☎ 20:37, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=425 bijection], id=425 -- WP: bijection -- Status: A

:: Paul August ☎ 15:03, Feb 2, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3484 Burali-Forti paradox], id=3484 -- WP: Burali-Forti paradox -- Status: A

:: Paul August ☎ 15:22, Feb 2, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3488 Cantor's paradox], id=3488 -- WP: Cantor's Theorem -- Status: A

::Actually the PM article is misnamed, it is really about "Cantor's Theorem". WP does not have an article about "Cantor's Paradox" but should. Paul August ☎ 02:21, Feb 3, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=359 cartesian product], id=359 -- WP: cartesian product -- Status: A

:: Paul August ☎ 02:25, Feb 3, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1344 chain], id=1344 -- WP: chain (mathematics) -- Status: A

:: Paul August ☎ 02:43, Feb 3, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=350 characteristic function], id=350 -- WP: indicator function -- Status: M

::Paul August ☎ 03:35, 10 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3277 concentric circles], id=3277 -- WP: concentric -- Status: A

::Paul August ☎ 03:08, Feb 3, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=533 conjunction], id=533 -- WP: logical conjunction -- Status: A

::Paul August ☎ 03:15, Feb 3, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2262 cycle], id=2262 -- WP: cycle (mathematics) -- Status: C

:: Paul August ☎ 21:27, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=604 disjoint], id=604 -- WP: disjoint -- Status: A

:: Paul August ☎ 00:08, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=382 empty set], id=382 -- WP: empty set -- Status: A

:: Paul August ☎ 00:10, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4703 even number], id=4703 -- WP: even number -- Status: A

:: Paul August ☎ 00:22, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2777 fixed point], id=2777 -- WP: fixed point (mathematics) -- Status: A

:: Paul August ☎ 00:22, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=881 infinite], id=881 -- WP: infinite -- Status: A

:: Paul August ☎ 03:49, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=429 injective function], id=429 -- WP: injective function -- Status: A

:: Paul August ☎ 03:49, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=403 integer], id=403 -- WP: integer -- Status: A

:: PM article gives a definition of the integers as an equivalence class on NxN. Also conntains some additional algebraic properties: integral domain, ordered ring, valuation. Paul August ☎ 03:49, Feb 4, 2005 (UTC)

:: I would say this should go in a separate article, called say construction of integers. This in order to keep the integer page elementary. We will discuss this more. Oleg Alexandrov | talk 20:36, 5 Feb 2005 (UTC)

::Well I've gone ahead and done the merging, including the bit on the construction from the natural numbers. If someone (Oleg?) wants to move this to its own article be my guest ;-) Paul August ☎ 20:38, 5 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4645 inverse function], id=4645 -- WP: inverse function -- Status: M

:: Merged. Paul August ☎ 21:14, 5 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5783 line segment], id=5783 -- WP: line segment -- Status: C

::Paul August ☎ 22:17, 5 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1345 linearly ordered], id=1345 -- WP: total order -- Status: A

:: Paul August ☎ 04:16, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1982 operator], id=1982 -- WP: operator -- Status: A

:: Paul August ☎ 04:32, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=358 ordered pair], id=358 -- WP: ordered pair -- Status: A

:: Paul August ☎ 04:32, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6617 ordered tuplet], id=6617 -- WP: n-tuple -- Status: A

:: Paul August ☎ 01:13, 6 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=444 ordering relation], id=444 -- WP: total order -- Status: A

:: Paul August ☎ 20:37, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=362 partition], id=362 -- WP: partition of a set -- Status: A

:: Paul August ☎ 20:57, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=434 permutation], id=434 -- WP: permutation -- Status: A

::Paul August ☎ 04:27, Feb 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4569 pullback], id=4569 -- WP: none -- Status: N

::I don't think we need this article. It seems really to be an article about function composition. I've never heard the term "pullback" used in this context. Paul August ☎ 15:28, 5 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=316 Russell's paradox], id=316 -- WP: Russell's paradox -- Status: A

::Paul August ☎ 22:51, Feb 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4562 set closed under an operation], id=4562 -- WP: closure (mathematics) -- Status: A

::Paul August ☎ 15:38, 5 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4061 signature of a permutation], id=4061 -- WP: even and odd permutations -- Status:

::The PM article contains a proposition and proof about the "signature of a permutation" which me may or may not want to include. Paul August ☎ 21:07, Feb 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2022 simple function], id=2022 -- WP: simple function -- Status: A

::Paul August ☎ 04:06, 10 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=472 subset], id=472 -- WP: subset -- Status: A

:: Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2791 surjective], id=2791 -- WP: surjective -- Status: A

:: Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2274 transposition], id=2274 -- WP: Transposition (mathematics) -- Status: C

:: Paul August ☎ 00:32, August 26, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=532 truth table], id=532 -- WP: truth table -- Status: A

:: Paul August ☎ 03:58, Feb 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7222 a surjection between finite sets of the same cardinality is bijective], id=7222 -- WP: bijection -- Status: A

::Paul August ☎ 01:38, 6 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6923 an injection between two finite sets of the same cardinality is bijective], id=6923 -- WP: bijection -- Status: A

::Paul August ☎ 01:38, 6 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7270 definition of onto linear transformation], id=7270 -- WP: linear transformation -- Status: A

:: Paul August ☎ 20:02, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7260 pointwise], id=7260 -- WP: pointwise -- Status: C

::Paul August ☎ 18:25, 3 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8320 (a,b)=(c,d) if and only if a=c and b=d], id=8320^new! -- WP guess: (a,b)=(c,d) if and only if a=c and b=d -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9621 characterization of signature of a permutation], id=9621^new! -- WP guess: characterization of signature of a permutation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8165 endpoint], id=8165^new! -- WP guess: endpoint -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9045 every permutation has a cycle decomposition], id=9045^new! -- WP guess: every permutation has a cycle decomposition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7808 example of an operator], id=7808^new! -- WP guess: example of an operator -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8680 example of bijection], id=8680^new! -- WP guess: example of bijection -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8277 fix], id=8277^new! -- WP guess: fix -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8973 partition is equivalent to an equivalence relation], id=8973^new! -- WP guess: partition is equivalent to an equivalence relation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9842 permutation notation], id=9842^new! -- WP guess: permutation notation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8218 properties of cardinal numbers], id=8218^new! -- WP guess: properties of cardinal numbers -- Status:

::All articles reviewed. Paul August ☎ 17:09, 7 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3088 axiom], id=3088 -- WP: axiom -- Status: M

::The PM article gives a better treatment for the historical development of the ideas of "axiom" and "postulate", which should be included in our article, in its own section called "Historical development". Paul August ☎ 17:09, 7 May 2006 (UTC)

::I've now merged this content. Paul August ☎ 22:12, 9 May 2006 (UTC)

::NM: 1. Paul August ☎ 20:53, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5392 CNF], id=5392 -- WP: Conjunctive normal form -- Status: A

::PM article is essentially empty. Paul August ☎ 03:50, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=891 contrapositive], id=891 -- WP: contrapositive -- Status: A

::Paul August ☎ 03:55, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=536 disjunction], id=536 -- WP: logical disjunction -- Status: A

::Paul August ☎ 04:56, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5677 DNF], id=5677 -- WP: Disjunctive normal form -- Status: A

::Paul August ☎ 05:01, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3769 equivalent], id=3769 -- WP: equivalent -- Status: A

::The PM article is empty. Paul August ☎ 05:10, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=480 implication], id=480 -- WP: logical conditional -- Status: A

::Paul August ☎ 05:28, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4379 Proof that contrapositive statement is true using logical equivalence], id=4379 -- WP: Contrapositive -- Status: A

::Paul August ☎ 05:34, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3475 propositional logic], id=3475 -- WP: propositional logic -- Status: A

:: Rich Farmbrough, 19:45 11 January 2007 (GMT).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3383 theory], id=3383 -- WP: Model theory -- Status: A

:: Paul August ☎ 21:04, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1618 transitive], id=1618 -- WP: transitive relation -- Status: A

:: Paul August ☎ 21:22, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=483 truth function], id=483 -- WP: truth function -- Status: M

::Alba 21:54, 25 Feb 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6853 every proposition is equivalent to a proposition in DNF], id=6853 -- WP: disjunctive normal form -- Status: A

::Paul August ☎ 01:49, 6 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7311 example of tautology], id=7311 -- WP: tautology (logic) -- Status: A

::Paul August ☎ 23:12, 3 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7310 tautology], id=7310 -- WP: tautology (logic) -- Status: A

::Paul August ☎ 23:03, 3 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8097 contradiction], id=8097^new! -- WP guess: contradiction -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8608 contradictory statement], id=8608^new! -- WP guess: contradictory statement -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9554 converse theorem], id=9554^new! -- WP guess: converse theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8529 examples of contrapositive], id=8529^new! -- WP guess: examples of contrapositive -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9093 inference rule], id=9093^new! -- WP guess: inference rule -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9686 inverse statement], id=9686^new! -- WP guess: inverse statement -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9240 logical axiom], id=9240^new! -- WP guess: logical axiom -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8605 logical connective], id=8605^new! -- WP guess: logical connective -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9092 modus ponens], id=9092^new! -- WP guess: modus ponens -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9200 modus tollens], id=9200^new! -- WP guess: modus tollens -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8195 necessary and sufficient], id=8195^new! -- WP guess: necessary and sufficient -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8619 negation], id=8619^new! -- WP guess: negation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9515 universal assumption], id=9515^new! -- WP guess: universal assumption -- Status:

::NM: 4. Paul August ☎ 04:51, 6 October 2005 (UTC)

::Needs to be reviewed: 25. Paul August ☎ 02:43, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3344 \Delta_1 bootstrapping], id=3344 -- WP guess: \Delta_1 bootstrapping -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3272 arithmetical hierarchy], id=3272 -- WP: arithmetical hierarchy -- Status: NM

::Paul August ☎ 18:33, Feb 6, 2005 (UTC)

:::Actually, this one needs more than a merge. Neither the WP article nor the PM article describes the arithmetical hierarchy on sets of reals, only on sets of naturals. They're pretty much the same thing from the descriptive set theoretic perspective, though not from the computability perspective. Article needs to be rewritten with the more inclusive descriptive set theory definitions, then the computability ones should be explained as consequences. --Trovatore 04:20, 6 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3273 arithmetical hierarchy is a proper hierarchy], id=3273 -- WP: arithmetical hierarchy -- Status: NM

:: Paul August ☎ 01:50, 30 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3002 atomic formula], id=3002 -- WP: Formula (mathematical logic) -- Status: A

:: Paul August ☎ 21:47, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=543 Boolean], id=543 -- WP: Boolean -- Status: A

::Paul August ☎ 20:37, Feb 6, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3043 creating an infinite model], id=3043 -- WP guess: creating an infinite model -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3035 criterion for consistency of sets of formulas], id=3035 -- WP guess: criterion for consistency of sets of formulas -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3348 deductions are \Delta_1], id=3348 -- WP guess: deductions are \Delta_1 -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3345 example of Gödel numbering], id=3345 -- WP: Gödel numbering -- Status: A

:: Paul August ☎ 22:00, 27 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2990 example of well-founded induction], id=2990 -- WP guess: example of well-founded induction -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2999 first order language], id=2999 -- WP: first-order language -- Status: A

::Currently first-order language is a redirect to first-order logic, which contains all this content, it could perhaps have its own article. Paul August ☎ 22:37, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3379 first order logic], id=3379 -- WP: first-order logic -- Status: A

:: Paul August ☎ 03:41, 6 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3012 first order theories], id=3012 -- WP guess: first-order theories -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3008 free and bound variables], id=3008 -- WP guess: free and bound variables -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3377 generalized quantifier], id=3377 -- WP guess: generalized quantifier -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3343 Gödel numbering], id=3343 -- WP: Gödel numbering -- Status: NM

::Paul August ☎ 21:17, Feb 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4580 Gödel's incompleteness theorems], id=4580 -- WP: Gödel's incompleteness theorems -- Status: NM

::Paul August ☎ 21:36, Feb 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6105 Herbrand structure], id=6105 -- WP: Herbrand structure -- Status: C

::copied by someone else. linas (talk) 22:31, 4 June 2008 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6104 Herbrand's theorem (first-order logic)], id=6104 -- WP: Herbrand's theorem -- Status: A

::Mathemens (talk) 22:16, 30 April 2008 (UTC) Someone has seemingly already covered this article. Changed status.

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2997 Lindenbaum algebra], id=2997 -- WP: Lindenbaum-Tarski algebra -- Status: A

:: Paul August ☎ 03:22, 6 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4556 Lindström's theorem], id=4556 -- WP guess: Lindström's theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3380 logic], id=3380 -- WP guess: logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3376 logical language], id=3376 -- WP guess: logical language -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3185 Presburger arithmetic], id=3185 -- WP: Presburger arithmetic -- Status: A

:: Paul August ☎ 03:10, 6 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3034 proof of compactness theorem for first-order logic], id=3034 -- WP guess: proof of compactness theorem for first-order logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2704 proof of principle of transfinite induction], id=2704 -- WP guess: proof of principle of transfinite induction -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2989 proof of the well-founded induction principle], id=2989 -- WP guess: proof of the well-founded induction principle -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3360 quantifier], id=3360 -- WP guess: quantifier -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4031 quantifier free], id=4031 -- WP guess: quantifier free -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2998 R-minimal element], id=2998 -- WP guess: R-minimal element -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3361 Skolemization], id=3361 -- WP guess: Skolemization -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3001 subformula], id=3001 -- WP guess: subformula -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3033 syntactic compactness theorem for first order logic], id=3033 -- WP guess: syntactic compactness theorem for first-order logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2703 transfinite induction], id=2703 -- WP: transfinite induction -- Status: A

::Paul August ☎ 03:54, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3342 universal relation], id=3342 -- WP guess: universal relation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3349 universal relations exist for each level of the arithmetical hierarchy], id=3349 -- WP guess: universal relations exist for each level of the arithmetical hierarchy -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2988 well-founded induction], id=2988 -- WP: Well-founded relation -- Status: NM

:: Paul August ☎ 02:43, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3000 well-founded induction on formulas], id=3000 -- WP guess: well-founded induction on formulas -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6852 prenex form], id=6852 -- WP: prenex normal form -- Status: A

:: Paul August ☎ 23:10, 3 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8746 fuzzy logic], id=8746^new! -- WP guess: fuzzy logic -- Status:

::Needs to be merged: 1. Paul August ☎ 05:17, Feb 17, 2005 (UTC)

::Needs to be reviewed: 4. Paul August ☎ 05:17, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3305 analytic hierarchy], id=3305 -- WP article: analytical hierarchy -- Status:

::PM article has erroneous title; we have the correct one. Our article still needs work. --Trovatore 05:00, 6 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3363 game-theoretical quantifier], id=3363 -- WP guess: game-theoretical quantifier -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3362 Härtig's quantifier], id=3362 -- WP guess: Härtig's quantifier -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4555 Russell's theory of types], id=4555 -- WP: type theory -- Status: NM

::Paul August ☎ 05:17, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3385 second order logic], id=3385 -- WP guess: second-order logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8747 point-free geometry], id=8747^new! -- WP guess: point-free geometry -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8646 consequence operator], id=8646^new! -- WP guess: consequence operator -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8671 consequence operator determined by a class of subsets], id=8671^new! -- WP guess: consequence operator determined by a class of subsets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8672 consequence operator is determined by its fixed points], id=8672^new! -- WP guess: consequence operator is determined by its fixed points -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8677 finiteness of C_\cup and C_{\cap}], id=8677^new! -- WP guess: finiteness of C_\cup and C_\cap -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8669 operations on consequence operators], id=8669^new! -- WP guess: operations on consequence operators -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8670 proof that C_\cup and C_\cap are consequence operators], id=8670^new! -- WP guess: proof that C_\cup and C_\cap are consequence operators -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8678 superfluity of the third defining property for finite consequence operator], id=8678^new! -- WP guess: superfluity of the third defining property for finite consequence operator -- Status:

::Needs to be merged: 2. Paul August ☎ 04:50, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2785 Church integer], id=2785 -- WP: Church integer -- Status: A

::Paul August ☎ 04:50, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2784 combinatory logic], id=2784 -- WP: combinatory logic -- Status: NM

::Paul August ☎ 04:45, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2788 lambda calculus], id=2788 -- WP: lambda calculus -- Status: NM

::Paul August ☎ 21:08, Feb 16, 2005 (UTC)

::Needs to be merged: 1. Paul August ☎ 04:51, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2097 conditional probability], id=2097 -- WP: conditional probability -- Status: A

::Paul August ☎ 04:10, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2263 induction], id=2263 -- WP: Mathematical induction -- Status: NM

::Paul August ☎ 04:04, Feb 13, 2005 (UTC)

::All articles processed. Paul August ☎ 05:10, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5843 neutrosophic logic], id=5843 -- WP: (none) -- Status: N

::Apparently deleted. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:10, 3 Feb 2005 (UTC).

::All articles processed. Paul August ☎ 05:11, Feb 17, 2005 (UTC)

::All articles processed. Paul August ☎ 05:12, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4158 standard enumeration], id=4158 -- WP guess: standard enumeration -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8354 more examples of Polish notation], id=8354^new! -- WP guess: more examples of Polish notation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8257 more examples of reverse Polish notation], id=8257^new! -- WP guess: more examples of reverse Polish notation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8243 Polish notation], id=8243^new! -- WP guess: Polish notation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8251 reverse Polish notation], id=8251^new! -- WP guess: reverse Polish notation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8256 shunting yard algorithm], id=8256^new! -- WP guess: shunting yard algorithm -- Status:

::Needs to be reviewed: 6. Paul August ☎ 03:01, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4559 Beth property], id=4559 -- WP guess: Beth property -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4557 compactness], id=4557 -- WP guess: compactness -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3386 consistent], id=3386 -- WP guess: consistent -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4732 Hofstadter's MIU system], id=4732 -- WP: none -- Status: N

:: Paul August ☎ 02:58, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4583 IF-logic], id=4583 -- WP guess: IF-logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4558 interpolation property], id=4558 -- WP guess: interpolation property -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3387 sentence], id=3387 -- WP: sentence (mathematical logic) -- Status: A

:: Paul August ☎ 03:01, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4552 Tarski's result on the undefinability of truth], id=4552 -- WP guess: Tarski's result on the undefinability of truth -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4464 Banach-Tarski paradox], id=4464 -- WP guess: Banach-Tarski paradox -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8201 paradox], id=8201^new! -- WP guess: paradox -- Status:

::Needs to be reviewed: 6. Paul August ☎ 05:06, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4486 congruence], id=4486 -- WP guess: congruence -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4541 every congruence is the kernel of a homomorphism], id=4541 -- WP guess: every congruence is the kernel of a homomorphism -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4488 homomorphic image of a \Sigma-structure is a \Sigma-structure], id=4488 -- WP guess: homomorphic image of a \Sigma-structure is a \Sigma-structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4485 kernel], id=4485 -- WP guess: kernel -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4519 kernel of a homomorphism is a congruence], id=4519 -- WP guess: kernel of a homomorphism is a congruence -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4487 quotient structure], id=4487 -- WP guess: quotient structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7235 Diamond Lemma], id=7235 -- WP guess: Diamond Lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9034 equational class], id=9034^new! -- WP guess: equational class -- Status:

::Needs to be reviewed: 20. Paul August ☎ 05:04, 28 May 2006 (UTC)

::NM: 2. Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1681 alphabet], id=1681 -- WP guess: alphabet -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3016 axiomatizable theory], id=3016 -- WP guess: axiomatizable theory -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4012 definable], id=4012 -- WP guess: definable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4064 definable type], id=4064 -- WP guess: definable type -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3394 downward Lowenheim-Skolem theorem], id=3394 -- WP:Löwenheim–Skolem theorem -- Status: NM

:: Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4070 example of definable type], id=4070 -- WP guess: example of definable type -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4030 example of strongly minimal], id=4030 -- WP guess: example of strongly minimal -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4582 first isomorphism theorem], id=4582 -- WP guess: first isomorphism theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1767 language], id=1767 -- WP guess: language -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2708 length of a string], id=2708 -- WP: string (computer science) -- Status: A

::in the "formal theory" section. CryptoDerk 20:18, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3049 models constructed from constants], id=3049 -- WP guess: models constructed from constants -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4489 proof of homomorphic image of a \Sigma-structure is a \Sigma-structure], id=4489 -- WP guess: proof of homomorphic image of a \Sigma-structure is a \Sigma-structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5733 relational structure], id=5733 -- WP guess: relational structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3032 satisfaction relation], id=3032 -- WP guess: satisfaction relation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4603 signature], id=4603 -- WP guess: signature -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3949 Stone space], id=3949 -- WP guess: Stone space -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4019 strongly minimal], id=4019 -- WP guess: strongly minimal -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3021 structure preserving mappings], id=3021 -- WP guess: structure preserving mappings -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3017 structures], id=3017 -- WP guess: structures -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2686 substring], id=2686 -- WP guess: substring -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4579 substructure], id=4579 -- WP guess: substructure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3913 type], id=3913 -- WP guess: type -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3393 upward Lowenheim-Skolem theorem], id=3393 -- WP: Löwenheim–Skolem theorem -- Status: NM

:: Paul August ☎ 05:04, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6843 theory of formal languages], id=6843 -- WP guess: theory of formal languages -- Status:

::All articles processed'''. Paul August ☎ 05:23, Feb 17, 2005 (UTC)

::'''Needs to be merged: 1. Paul August ☎ 05:27, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4137 random graph (infinite)], id=4137 -- WP: random graph -- Status: NM

::Paul August ☎ 05:27, Feb 17, 2005 (UTC)

::All articles processed. Paul August ☎ 05:35, Feb 17, 2005 (UTC)

::Needs to be merged: 2. Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3390 \kappa-categorical], id=3390 -- WP: Categorical (model theory) -- Status: A

::Arthur Rubin 21:25, 22 August 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3395 proof of Vaught's test], id=3395 -- WP: Model theory -- Status: NM

::Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3391 Vaught's test], id=3391 -- WP: Model theory -- Status: NM

::Paul August ☎ 05:42, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7045 countably categorical structures], id=7045 -- WP guess: countably categorical structures -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7044 oligomorphic permutation group], id=7044 -- WP guess: oligomorphic permutation group -- Status:

::All articles processed. Paul August ☎ 05:43, Feb 17, 2005 (UTC)

::Needs to be reviewed: 3. Paul August ☎ 05:46, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3925 example of a universal structure], id=3925 -- WP guess: example of a universal structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3923 homogeneous], id=3923 -- WP guess: homogeneous -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3922 universal structure], id=3922 -- WP guess: universal structure -- Status:

::Needs to be reviewed: 1. Paul August ☎ 05:47, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3964 amalgamation property], id=3964 -- WP guess: amalgamation property -- Status:

::Needs to be reviewed: 1. Paul August ☎ 05:50, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5736 automatic presentation], id=5736 -- WP guess: automatic presentation -- Status:

::Needs to be merged: 1. Paul August ☎ 05:57, Feb 17, 2005 (UTC)

::Needs to be reviewed: 2. Paul August ☎ 05:57, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3918 infinitesimal], id=3918 -- WP guess: infinitesimal -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3919 o-minimality], id=3919 -- WP guess: o-minimality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3920 real closed fields], id=3920 -- WP: real closed field -- Status: NM

::Paul August ☎ 02:23, Feb 14, 2005 (UTC)

::Needs to be reviewed: 1. Paul August ☎ 05:58, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3990 imaginaries], id=3990 -- WP guess: imaginaries -- Status:

::All articles processed. Paul August ☎ 05:58, Feb 17, 2005 (UTC)

::All articles processed. Paul August ☎ 05:14, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3184 Boolean valued model], id=3184 -- WP: Boolean-valued model -- Status: A

:: Paul August ☎ 05:14, 28 May 2006 (UTC)

::All articles processed. Paul August ☎ 06:00, Feb 17, 2005 (UTC)

::Needs to be merged: 5. Paul August ☎ 06:01, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3485 axiom of foundation], id=3485 -- WP: axiom of regularity -- Status: NM

::Paul August ☎ 01:27, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3388 elementarily equivalent], id=3388 -- WP: elementarily equivalent -- Status: NM

::A bit of notation could be merged. Paul August ☎ 01:37, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3389 elementary embedding], id=3389 -- WP: elementary embedding -- Status: NM

::Paul August ☎ 01:53, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3384 model], id=3384 -- WP: model theory -- Status: NM

::Or perhaps it could be copied to say: Model (model theory). Paul August ☎ 01:58, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3487 proof equivalence of formulation of foundation], id=3487 -- WP: axiom of regularity -- Status: NM

::Paul August ☎ 02:00, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8616 model theory], id=8616^new! -- WP guess: model theory -- Status:

::Needs to be merged: 1. Paul August ☎ 19:58, Feb 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2550 automaton], id=2550 -- WP: finite state machine -- Status: NM

::Paul August ☎ 02:46, Feb 14, 2005 (UTC)

::Needs to be merged: 4. Paul August ☎ 06:02, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2553 deterministic finite automaton], id=2553 -- WP: deterministic finite state machine -- Status: NM

::Paul August ☎ 02:34, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2557 non-deterministic finite automaton], id=2557 -- WP: nondeterministic finite state machine -- Status: NM

::Paul August ☎ 02:39, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2571 non-deterministic pushdown automaton], id=2571 -- WP: pushdown automaton -- Status: NM

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2800 Turing computable], id=2800 -- WP: computable function -- Status: A

::Paul August ☎ 03:08, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3357 Turing machine], id=3357 -- WP: Turing machine -- Status: NM

::Paul August ☎ 03:01, Feb 14, 2005 (UTC)

::Needs to be merged: 3. Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6139 alternative characterizations of recursive functions], id=6139 -- WP: recursive function -- Status: NM

:: Paul August ☎ 06:20, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6140 pairing function], id=6140 -- WP: pairing function -- Status: NM

::Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2801 primitive recursive], id=2801 -- WP: primitive recursive -- Status: A

::Paul August ☎ 06:12, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=664 recurrence relation], id=664 -- WP: recurrence relation -- Status: A

::Paul August ☎ 06:18, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6135 recursive function], id=6135 -- WP: recursive function -- Status: NM

::Paul August ☎ 06:24, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8983 characterization of primitive recursive functions of one variable], id=8983^new! -- WP guess: characterization of primitive recursive functions of one variable -- Status:

::Needs to be merged: 2. Paul August ☎ 19:59, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4170 computable number], id=4170 -- WP: computable number -- Status: NM

::Paul August ☎ 19:55, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3045 recursively enumerable], id=3045 -- WP: recursively enumerable set -- Status: NM

::Paul August ☎ 19:59, Feb 17, 2005 (UTC)

::All articles processed. Paul August ☎ 20:17, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2799 Ackermann function], id=2799 -- WP: Ackermann function -- Status: A

::Paul August ☎ 20:11, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1622 halting problem], id=1622 -- WP: halting problem -- Status: A

::Paul August ☎ 20:17, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9391 Penrose's first Gödelian argument], id=9391^new! -- WP guess: Penrose's first Gödelian argument -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9392 Penrose's second Gödelian argument], id=9392^new! -- WP guess: Penrose's second Gödelian argument -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9422 strong AI thesis], id=9422^new! -- WP guess: strong AI thesis -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9423 weak AI thesis], id=9423^new! -- WP guess: weak AI thesis -- Status:

::All articles processed. Paul August ☎ 00:05, August 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1620 perfect ruler], id=1620 -- WP: perfect ruler -- Status: C

::Rich Farmbrough 22:43, 22 August 2005 (UTC)

::This is related to but different from Golomb ruler. Paul August ☎ 20:36, Feb 17, 2005 (UTC)

::Needs to be merged: 5. Paul August ☎ 04:53, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4626 another definition of cofinality], id=4626 -- WP: cofinality -- Status: NM

::Paul August ☎ 20:51, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2205 cofinality], id=2205 -- WP: cofinality -- Status: NM

::Paul August ☎ 20:51, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2749 maximal element], id=2749 -- WP: maximal element -- Status: NM

::Paul August ☎ 20:59, Feb 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6118 minimal and maximal number], id=6118 -- WP: greatest element -- Status: NM

::Paul August ☎ 04:24, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3287 partitions less than cofinality], id=3287 -- WP: cofinality -- Status: NM

::Paul August ☎ 04:26, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=271 well ordered set], id=271 -- WP: well ordered -- Status: A

::Paul August ☎ 04:53, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7593 visualizing maximal elements], id=7593 -- WP guess: visualizing maximal elements -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9569 frequently in], id=9569^new! -- WP guess: frequently in -- Status:

::Needs to be merged: 3. Paul August ☎ 05:09, Feb 18, 2005 (UTC)

::Needs to be reviewed: 8. Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3212 antichain], id=3212 -- WP: antichain -- Status: NM

::Paul August ☎ 04:57, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3217 Aronszajn tree], id=3217 -- WP guess: Aronszajn tree -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3211 branch], id=3211 -- WP guess: branch -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3366 Erdős-Rado theorem], id=3366 -- WP guess: Erdős-Rado theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3219 example of Aronszajn tree], id=3219 -- WP guess: example of Aronszajn tree -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3213 example of tree (set theoretic)], id=3213 -- WP guess: example of tree (set theoretic) -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=502 pigeonhole principle], id=502 -- WP: pigeonhole principle -- Status: NM

::Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4106 proof of pigeonhole principle], id=4106 -- WP: pigeonhole principle -- Status: NM

::Paul August ☎ 05:09, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3218 proof that \omega has the tree property], id=3218 -- WP guess: proof that \omega has the tree property -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3220 Suslin tree], id=3220 -- WP guess: Suslin tree -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3210 tree (set theoretic)], id=3210 -- WP guess: tree (set theoretic) -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8086 another proof of pigeonhole principle], id=8086^new! -- WP guess: another proof of pigeonhole principle -- Status:

::NM: 14. Paul August ☎ 17:07, August 26, 2005 (UTC)

::Needs to be reviewed: 11. Paul August ☎ 03:22, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3230 \kappa-complete], id=3230 -- WP guess: \kappa-complete -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4056 additively indecomposable], id=4056 -- WP: additively indecomposable ordinal -- Status: C

:: Mathemens (talk) 22:32, 30 April 2008 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5710 aleph numbers], id=5710 -- WP: aleph number -- Status: NM

::Paul August ☎ 05:32, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5740 beth numbers], id=5740 -- WP: beth number -- Status: NM

::Paul August ☎ 05:32, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2109 Cantor's diagonal argument], id=2109 -- WP: Cantor's diagonal argument -- Status: NM

::Paul August ☎ 15:10, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3051 Cantor's theorem], id=3051 -- WP: Cantor's theorem -- Status: A

::Paul August ☎ 15:30, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5701 cardinal arithmetic], id=5701 -- WP: cardinal number -- Status: NM

::Paul August ☎ 15:46, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6584 cardinal exponentiation under GCH], id=6584 -- WP: cardinal number -- Status: NM

::Paul August ☎ 15:48, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1302 cardinal number], id=1302 -- WP: cardinal number -- Status: A

::Paul August ☎ 15:56, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5439 cardinal successor], id=5439 -- WP: successor cardinal -- Status: A

::Paul August ☎ 15:58, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=963 cardinality], id=963 -- WP: cardinality -- Status: NM

::Paul August ☎ 16:07, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=934 cardinality of a countable union], id=934 -- WP: countable set -- Status: A

::Paul August ☎ 16:12, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5708 cardinality of the continuum], id=5708 -- WP: cardinality of the continuum -- Status: M

:: Paul August ☎ 01:04, August 26, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=921 cardinality of the rationals], id=921 -- WP: rational number -- Status: A

::Paul August ☎ 16:46, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4053 classes of ordinals and enumerating functions], id=4053 -- WP guess: classes of ordinals and enumerating functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3227 club], id=3227 -- WP: club set -- Status: M

::Porcher 17:06, 3 Apr 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3231 club filter], id=3231 -- WP: club filter -- Status: C

::Porcher 16:56, 3 Apr 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=880 countable], id=880 -- WP: countable set -- Status: A

::Paul August ☎ 18:32, Feb 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=883 countably infinite], id=883 -- WP: countable set -- Status: A

::Paul August ☎ 22:05, Feb 19, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=500 finite], id=500 -- WP: finite -- Status: A

::Paul August ☎ 22:07, Feb 19, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4054 fixed points of normal functions], id=4054 -- WP guess: fixed points of normal functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3232 Fodor's lemma], id=3232 -- WP: Fodor's lemma -- Status: C

::This PM article along with the PM article "Proof of Fordor's lemma" has been copied to Fodor's lemma and mildly edited. Porcher 16:55, 1 Apr 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3954 height of an algebraic number], id=3954 -- WP guess: height of an algebraic number -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5781 Hilbert's hotel], id=5781 -- WP: Hilbert's paradox of the Grand Hotel -- Status: A

::Paul August ☎ 20:26, Feb 20, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4199 if A is infinite and B is a finite subset of A\,\!, then A\setminus B is infinite], id=4199 -- WP: Countable set -- Status: NM

::Paul August ☎ 16:02, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5598 König's theorem], id=5598 -- WP: König's theorem -- Status: NM

::The PM article has a proof of the theorem. Paul August ☎ 21:05, Feb 20, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5438 limit cardinal], id=5438 -- WP: limit cardinal -- Status: A

::Paul August ☎ 21:12, Feb 20, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=387 natural number], id=387 -- WP: natural number -- Status: A

::Paul August ☎ 21:20, Feb 20, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4052 ordinal arithmetic], id=4052 -- WP: ordinal number -- Status: NM

::Paul August ☎ 03:26, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1300 ordinal number], id=1300 -- WP: ordinal number -- Status: A

::Paul August ☎ 03:20, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=136 power set], id=136 -- WP: power set -- Status: NM

::Paul August ☎ 03:30, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3053 proof of Cantor's theorem], id=3053 -- WP: Cantor's theorem -- Status: A

::Paul August ☎ 03:34, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4055 proof of fixed points of normal functions], id=4055 -- WP guess: proof of fixed points of normal functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3234 proof of Fodor's lemma], id=3234 -- WP: Fodor's lemma -- Status: C

::This PM article along with the PM article "Fordor's lemma" has been copied to Fodor's lemma and mildly edited. Porcher 16:58, 1 Apr 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3156 proof of Schroeder-Bernstein theorem], id=3156 -- WP: Cantor–Bernstein–Schroeder theorem -- Status: A

::The PM proof is more detailed and could perhaps be merged. Paul August ☎ 04:03, Mar 13, 2005 (UTC)

::The PM proof is actually just plain different. I added a link to the WP article, that should suffice. linas 04:42, 24 November 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3955 proof of the existence of transcendental numbers], id=3955 -- WP guess: transcendental number -- Status: NM

::Paul August ☎ 04:09, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4057 proof of theorems in additively indecomposable], id=4057 -- WP guess: proof of theorems in additively indecomposable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=935 proof that countable unions are countable], id=935 -- WP: Countable set -- Status: A

::This proof could be merged into Countable set. Paul August ☎ 15:07, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=927 proof that the rationals are countable], id=927 -- WP guess: proof that the rationals are countable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2091 Schroeder-Bernstein theorem], id=2091 -- WP: Cantor–Bernstein–Schroeder theorem -- Status: A

::Paul August ☎ 04:03, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=397 sequence], id=397 -- WP: sequence -- Status: NM

::The PM article contains a generalization of sequence to a function whose domain is any ordinal, not just N. Paul August ☎ 20:13, Mar 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3228 stationary set], id=3228 -- WP: stationary set -- Status: A

::This article has been copied prom the PM original and classified as a stub. Porcher 17:09, 1 Apr 2005 (UTC)

::This article no longer uses any PM text, so I've changed the status to "A". Paul August ☎ 16:05, 21 February 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=385 successor], id=385 -- WP guess: successor -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5440 successor cardinal], id=5440 -- WP: successor cardinal -- Status: A

::Paul August ☎ 02:45, Mar 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=884 uncountable], id=884 -- WP: uncountable set -- Status: A

::Paul August ☎ 03:58, Mar 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4058 Veblen function], id=4058 -- WP guess: Veblen function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2786 von Neumann integer], id=2786 -- WP: Natural number -- Status: NM

::The PM article uses the term "von Neumann integer", not used in WP. Paul August ☎ 03:05, Mar 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2787 von Neumann ordinal], id=2787 -- WP: ordinal -- Status: NM

::The PM article uses the term "von Neumann ordinal", not used in WP. Paul August ☎ 03:05, Mar 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3177 weakly compact cardinal], id=3177 -- WP: weakly compact cardinal -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3223 weakly compact cardinals and the tree property], id=3223 -- WP: weakly compact cardinal -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6999 algebraic numbers are countable], id=6999 -- WP guess: algebraic numbers are countable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7003 all algebraic numbers in a sequence], id=7003 -- WP guess: all algebraic numbers in a sequence -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7448 Cantor Normal Form], id=7448 -- WP guess: Cantor Normal Form -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7451 normal (ordinal) function], id=7451 -- WP guess: normal (ordinal) function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7142 the cartesian product of a finite number of countable sets is countable], id=7142 -- WP guess: the cartesian product of a finite number of countable sets is countable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8073 another proof of cardinality of the rationals], id=8073^new! -- WP guess: another proof of cardinality of the rationals -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8696 cardinality of disjoint union of finite sets], id=8696^new! -- WP guess: cardinality of disjoint union of finite sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9327 intercession], id=9327^new! -- WP guess: intercession -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9089 motivation for von Neumann ordinals], id=9089^new! -- WP guess: motivation for von Neumann ordinals -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7675 open and closed intervals have the same cardinality], id=7675^new! -- WP guess: open and closed intervals have the same cardinality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7721 subsets of countable sets are countable], id=7721^new! -- WP guess: subsets of countable sets are countable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8206 the set of all real transcendental numbers is uncountable], id=8206^new! -- WP guess: the set of all real transcendental numbers is uncountable -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8603 uniqueness of cardinality], id=8603^new! -- WP guess: uniqueness of cardinality -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6516 axiom of determinacy], id=6516 -- WP: axiom of determinacy -- Status: A

:: … (former caveats have been rectified by Determinacy article) --Trovatore 03:17, 7 September 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6736 Cantor-Bendixson derivative], id=6736 -- WP: Cantor-Bendixson derivative -- Status: A

:: Mathemens (talk) 22:34, 30 April 2008 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6737 Cantor-Bendixson theorem], id=6737 -- WP: Cantor-Bendixson theorem -- Status: A

:: Paul August ☎ 05:29, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9332 paradox of the binary tree], id=9332^new! -- WP guess: paradox of the binary tree -- Status:

::All articles processed. Paul August ☎ 03:37, Mar 14, 2005 (UTC)

::Needs to be merged: 15. Paul August ☎ 17:03, August 25, 2005 (UTC)

::Needs to be copied: 2. Paul August ☎ 17:03, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3400 additive], id=3400 -- WP: sigma additivity -- Status: C

:: Paul August ☎ 00:48, August 27, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1666 antisymmetric], id=1666 -- WP: antisymmetric -- Status: A

::The PM article gives some finite examples, and gives fromulas for the number of relations and antisymmetric relations on a set with n elements. This content could be included, but I'm not sure it needs to be. Paul August ☎ 14:37, Mar 15, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6226 complex function], id=6226 -- WP: complex analysis -- Status: A

::The PM articles content is covered in complex analysis, real part and imaginary part. We could, however, make complex function its own article. Paul August ☎ 13:45, Mar 17, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4727 constant function], id=4727 -- WP: constant function -- Status: M

::Paul August ☎ 04:54, Mar 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5792 dependence relation], id=5792 -- WP: dependence relation -- Status: NC

:: This topic is related to Matroids. Paul August ☎ 16:50, August 25, 2005 (UTC)

::: The only article linking to dependence relation is on using the term in a way that suggests redirecting to statistical independence, not the concept occuring in matroid theory. Should this become a disambiguation page? Michael Hardy 20:49, August 31, 2005 (UTC)

:::: Perhaps, I don't know much about this. Paul August ☎ 22:54, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=443 direct image], id=443 -- WP: image (mathematics) -- Status: A

::Paul August ☎ 05:06, Mar 18, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=966 domain], id=966 -- WP: domain (mathematics) -- Status: NM

::The PM article contains the more general notion of domain of a relation. Paul August ☎ 01:02, Apr 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2024 dynkin system], id=2024 -- WP: Dynkin system -- Status: C

:: Paul August ☎ 01:56, August 27, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=468 equivalence class], id=468 -- WP: equivalence class -- Status: A

::Paul August ☎ 01:12, Apr 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3276 fibre], id=3276 -- WP: Image (mathematics) -- Status: M

::Paul August ☎ 02:26, Apr 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1331 filtration], id=1331 -- WP: filtration (abstract algebra) -- Status: A

::Paul August ☎ 16:15, Apr 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3692 finite character], id=3692 -- WP: set system of finite character -- Status: C

:: Paul August ☎ 02:59, August 27, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2510 fix (transformation actions)], id=2510 -- WP: transformation (mathematics) -- Status: NM

:: Paul August ☎ 16:27, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=360 function], id=360 -- WP: function (mathematics) -- Status: A

::Paul August ☎ 03:41, Apr 29, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2722 functional], id=2722 -- WP: functional -- Status: A

::Paul August ☎ 13:23, August 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=361 generalized cartesian product], id=361 -- WP: Cartesian product -- Status: M

::Paul August ☎ 18:34, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3701 graph], id=3701 -- WP: graph of a function -- Status: A

::Paul August ☎ 20:37, Apr 23, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5418 identity map], id=5418 -- WP: identity function -- Status: NM

::Paul August ☎ 15:38, August 5, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4402 inclusion mapping], id=4402 -- WP: inclusion map -- Status: A

:: Paul August ☎ 01:32, August 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=386 inductive set], id=386 -- WP: inductive set (axiom of infinity) -- Status: C

:: PM article is just a definition, but [http://mathworld.wolfram.com/InductiveSet.html Mathworld] has a nice article. Paul August ☎ 01:33, August 28, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2504 invariant], id=2504 -- WP: invariant -- Status: NM

:: Paul August ☎ 17:45, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3346 inverse function theorem], id=3346 -- WP: inverse function theorem -- Status: NM

:: Paul August ☎ 17:50, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=442 inverse image], id=442 -- WP: image (mathematics) -- Status: NM

:: Paul August ☎ 17:55, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5668 law of trichotomy], id=5668 -- WP: trichotomy -- Status: A

:: I think the WP article needs some work though. Paul August ☎ 18:12, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1349 left function notation], id=1349 -- WP: mathematical function -- Status: NM

:: Or perhaps merged with the PM article [http://planetmath.org/?op=getobj&from=objects&id=1351 right function notation] (below) into it's own article say function notation. Paul August ☎ 16:14, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6569 level set], id=6569 -- WP: level set -- Status: NM

:: PM defines level set as a synonym of fiber. Our article has a more restrictive definition. I don't know which is more correct, but this should be reconciled, and if the fiber definition is common, it should be mentioned in our article. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1975 mapping], id=1975 -- WP: map (mathematics) -- Status: A

:: Paul August ☎ 19:05, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4540 mapping of period n is a bijection], id=4540 -- WP: function composition -- Status: NM

:: Paul August ☎ 19:41, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6653 operation], id=6653 -- WP: operator -- Status: A

:: Paul August ☎ 19:48, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3341 partial function], id=3341 -- WP: partial function -- Status: A

:: Paul August ☎ 20:34, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4768 partial mapping], id=4768 -- WP: partial mapping -- Status: NM

::partial mapping redirects to partial function. The PM article is about an entirely different thing, which should probably be merged into WP in some form. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4539 period of mapping], id=4539 -- WP: function composition -- Status: NM

:: Paul August ☎ 19:41, August 7, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2037 pi-system], id=2037 -- WP: pi-system -- Status: A

:: Paul August ☎ 17:18, August 8, 2005 (UTC)

::NC changed to A, its now in WP of its own accord. linas 04:49, 24 November 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4112 proof of inverse function theorem], id=4112 -- WP: inverse function theorem -- Status: NM

:: This proof might (or might not) be useful. Paul August ☎ 16:13, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6192 proof of the associativity of the symmetric difference operator], id=6192 -- WP: none -- Status: N

:: Paul August ☎ 17:28, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=501 proper subset], id=501 -- WP: proper subset -- Status: A

::Paul August ☎ 03:25, Apr 29, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=967 range], id=967 -- WP: range (mathematics) -- Status: NM

:: The PM article defines the more general notion of range of a relation. Paul August ☎ 19:27, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1644 reflexive], id=1644 -- WP: reflexive -- Status: A

:: Paul August ☎ 19:39, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=122 relation], id=122 -- WP: relation (mathematics) -- Status: A

:: Paul August ☎ 20:03, August 8, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4401 restriction], id=4401 -- WP: function (mathematics) -- Status: A

:: Paul August ☎ 21:07, August 10, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1351 right function notation], id=1351 -- WP: function (mathematics) -- Status: NM

:: Or perhaps merged with the PM article [http://planetmath.org/?op=getobj&from=objects&id=1349 left function notation] (above) into it's own article say function notation. Paul August ☎ 16:14, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=913 set difference], id=913 -- WP: complement (set theory) -- Status: A

::Paul August ☎ 19:06, May 20, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1647 symmetric], id=1647 -- WP: symmetric relation -- Status: A

:: Paul August ☎ 01:39, August 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=916 symmetric difference], id=916 -- WP: symmetric difference -- Status: A

:: Paul August ☎ 01:51, August 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4213 the inverse image commutes with set operations], id=4213 -- WP: image (mathematics) -- Status: NM

:: Paul August ☎ 16:18, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1977 transformation], id=1977 -- WP: transformation (mathematics) -- Status: A

:: Paul August ☎ 01:59, August 16, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1565 transitive], id=1565 -- WP: transitive set -- Status: A

:: Paul August ☎ 03:38, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1669 transitive], id=1669 -- WP: transitive relation -- Status: A

:: Paul August ☎ 03:41, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3486 transitive closure], id=3486 -- WP: transitive set -- Status: A

:: PM gives a construction of the transitive closure of a set and our article should probably include one, but I'm not sure that the PM one is correct. Paul August ☎ 15:58, August 25, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7140 antiderivative of complex function], id=7140 -- WP: antiderivative of complex function -- Status: A

: I wrote a new article inspired by the PM article. Oleg Alexandrov (talk) 01:49, 21 July 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7247 Characterization of basis of finite dimensional vector space], id=7247 -- WP guess: Characterization of basis of finite dimensional vector space -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7088 constant functions and continuity], id=7088 -- WP guess: constant functions and continuity -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7148 level sets of smooth functions on manifolds], id=7148 -- WP guess: level sets of smooth functions on manifolds -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6715 limit of sequence of sets], id=6715 -- WP guess: limit of sequence of sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6705 properties of functions], id=6705 -- WP guess: properties of functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8185 argument], id=8185^new! -- WP guess: argument -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8429 criterion for a set to be transitive], id=8429^new! -- WP guess: criterion for a set to be transitive -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8044 example of antisymmetric], id=8044^new! -- WP guess: example of antisymmetric -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9586 example of law of trichotomy on <], id=9586^new! -- WP guess: example of law of trichotomy on < -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7759 examples of ring of sets], id=7759^new! -- WP guess: examples of ring of sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7758 finite fields of sets], id=7758^new! -- WP guess: finite fields of sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7639 irreflexive], id=7639^new! -- WP guess: irreflexive -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8600 operations on relations], id=8600^new! -- WP guess: operations on relations -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7936 pointed set], id=7936^new! -- WP guess: pointed set -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7710 product], id=7710^new! -- WP guess: product -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8497 properties of a function], id=8497^new! -- WP guess: properties of a function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8879 properties of injective functions], id=8879^new! -- WP guess: properties of injective functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8509 quasi-inverse of a function], id=8509^new! -- WP guess: quasi-inverse of a function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7757 ring of sets], id=7757^new! -- WP guess: ring of sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8884 Schröeder Bernstein Theorem: Proof], id=8884^new! -- WP guess: Schröeder Bernstein Theorem: Proof -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9781 well-founded relation], id=9781^new! -- WP guess: well-founded relation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=310 axiom of choice], id=310 -- WP: axiom of choice -- Status: NM

:: Paul August ☎ 20:37, August 28, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6418 axiom of countable choice], id=6418 -- WP: axiom of countable choice -- Status: M

:: Paul August ☎ 21:42, August 28, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6419 choice function], id=6419 -- WP: choice function -- Status: M

:: Paul August ☎ 00:24, August 29, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3493 Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle], id=3493 -- WP guess: Zorn's lemma and the well-ordering theorem equivalence of Hausdorff's maximum principle -- Status: NC

::Needs to be copied or merged into some article, not sure where. linas 02:36, 8 April 2007 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3358 equivalence of Zorn's lemma and the axiom of choice], id=3358 -- WP: Zorn's lemma -- Status: NM

:: Zorn's lemma has a sketch of a proof that AC implies Zorn, I think it would be good to include the reverse implication. Paul August ☎ 04:07, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3491 Hausdorff's maximum principle], id=3491 -- WP: Hausdorff maximality theorem -- Status: A

:: PM has a proof using Zorn's lemma, which would be good to include. Paul August ☎ 04:45, August 31, 2005 (UTC)

::Changed from NM to A, as I just added text that is more or less equivalent, I think. linas 02:18, 8 April 2007 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3695 Kuratowski's lemma], id=3695 -- WP guess: Kuratowski's lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2533 maximality principle], id=2533 -- WP guess: maximality principle -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6428 permutation model], id=6428 -- WP guess: permutation model -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=245 principle of finite induction], id=245 -- WP: mathematical induction -- Status: A

:: Paul August ☎ 20:20, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=337 principle of finite induction proven from well-ordering principle], id=337 -- WP guess: principle of finite induction proven from well-ordering principle -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4672 proof of Tukey's lemma], id=4672 -- WP guess: proof of Tukey's lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3359 proof of Zermelo's well-ordering theorem], id=3359 -- WP: well-ordering theorem -- Status: NM

:: Paul August ☎ 20:29, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3693 Tukey's lemma], id=3693 -- WP: Tukey's lemma -- Status: A

::Paul August ☎ 02:51, 18 August 2009 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3694 Zermelo's postulate], id=3694 -- WP guess: Zermelo's postulate -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3354 Zermelo's well-ordering theorem], id=3354 -- WP: well-ordering theorem -- Status: A

:: Paul August ☎ 19:45, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1341 Zorn's lemma], id=1341 -- WP: Zorn's lemma -- Status: A

:: Paul August ☎ 04:01, August 31, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7057 Hausdorff paradox], id=7057 -- WP guess: Hausdorff paradox -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7123 proof of Banach-Tarski paradox], id=7123 -- WP guess: proof of Banach-Tarski paradox -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7059 proof of Hausdorff paradox], id=7059 -- WP guess: proof of Hausdorff paradox -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7241 relation as union of functions], id=7241 -- WP guess: relation as union of functions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8604 one-to-one function from onto function], id=8604^new! -- WP guess: one-to-one function from onto function -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8342 proof of Zermelo's postulate], id=8342^new! -- WP guess: proof of Zermelo's postulate -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8763 proof that a relation is union of functions if and only if AC], id=8763^new! -- WP guess: proof that a relation is union of functions if and only if AC -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8792 selector], id=8792^new! -- WP guess: selector -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8835 well-ordering principle for natural numbers proven from the principle of finite induction], id=8835^new! -- WP guess: well-ordering principle for natural numbers proven from the principle of finite induction -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8200 well-ordering principle implies axiom of choice], id=8200^new! -- WP guess: well-ordering principle implies axiom of choice -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5658 \mathcal{U}-small], id=5658 -- WP guess: \mathcalU-small -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4391 axiom of extensionality], id=4391 -- WP: axiom of extensionality -- Status: A

::Paul August ☎ 04:17, Apr 29, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4419 axiom of infinity], id=4419 -- WP: axiom of infinity -- Status: NM

:: Paul August ☎ 02:35, 8 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4392 axiom of pairing], id=4392 -- WP: axiom of pairing -- Status: A

:: Paul August ☎ 01:31, September 4, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4399 axiom of power set], id=4399 -- WP: axiom of power set -- Status: M

:: Paul August ☎ 19:09, 14 September 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4394 axiom of union], id=4394 -- WP: axiom of union -- Status: A

::Paul August ☎ 02:30, 8 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4393 axiom schema of separation], id=4393 -- WP: axiom schema of separation -- Status: A

:: Paul August ☎ 02:26, 15 September 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2308 de Morgan's laws], id=2308 -- WP guess: de Morgan's laws -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4134 de Morgan's laws for sets (proof)], id=4134 -- WP guess: de Morgan's laws for sets (proof) -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5569 example of universe], id=5569 -- WP guess: example of universe -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3866 set theory], id=3866 -- WP guess: set theory -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1619 union], id=1619 -- WP: union (set theory) -- Status: A

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4107 universe], id=4107 -- WP guess: universe -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4395 von Neumann-Bernays-Gödel set theory], id=4395 -- WP guess: von Neumann-Bernays-Gödel set theory -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6747 example of universe of finite sets], id=6747 -- WP guess: example of universe of finite sets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7544 proof of properties of universe], id=7544 -- WP guess: proof of properties of universe -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7548 Tarski's axiom], id=7548 -- WP guess: Tarski's axiom -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8883 index of set theory], id=8883^new! -- WP guess: index of set theory -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9800 well-foundedness and axiom of foundation], id=9800^new! -- WP guess: well-foundedness and axiom of foundation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3241 chain condition], id=3241 -- WP guess: chain condition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3256 composition of forcing notions], id=3256 -- WP guess: composition of forcing notions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3262 composition preserves chain condition], id=3262 -- WP guess: composition preserves chain condition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3257 equivalence of forcing notions], id=3257 -- WP guess: equivalence of forcing notions -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3039 forcing], id=3039 -- WP guess: forcing -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3238 forcing relation], id=3238 -- WP guess: forcing relation -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3263 forcings are equivalent if one is dense in the other], id=3263 -- WP guess: forcings are equivalent if one is dense in the other -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3314 FS iterated forcing preserves chain condition], id=3314 -- WP guess: FS iterated forcing preserves chain condition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3264 iterated forcing], id=3264 -- WP guess: iterated forcing -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3265 iterated forcing and composition], id=3265 -- WP guess: iterated forcing and composition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3242 partial order with chain condition does not collapse cardinals], id=3242 -- WP guess: partial order with chain condition does not collapse cardinals -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3243 proof of partial order with chain condition does not collapse cardinals], id=3243 -- WP guess: proof of partial order with chain condition does not collapse cardinals -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3258 proof that forcing notions are equivalent to their composition], id=3258 -- WP guess: proof that forcing notions are equivalent to their composition -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3239 complete partial orders do not add small subsets], id=3239 -- WP guess: complete partial orders do not add small subsets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3240 proof of complete partial orders do not add small subsets], id=3240 -- WP guess: proof of complete partial orders do not add small subsets -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3247 \Diamond is equivalent to \clubsuit and continuum hypothesis], id=3247 -- WP guess: \Diamond is equivalent to \clubsuit and continuum hypothesis -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3244 Levy collapse], id=3244 -- WP guess: Levy collapse -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3248 proof of \Diamond is equivalent to \clubsuit and continuum hypothesis], id=3248 -- WP guess: proof of \Diamond is equivalent to \clubsuit and continuum hypothesis -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4647 a shorter proof: Martin's axiom and the continuum hypothesis], id=4647 -- WP guess: a shorter proof: Martin's axiom and the continuum hypothesis -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1183 continuum hypothesis], id=1183 -- WP: continuum hypothesis -- Status: A

:: Trovatore 15:25, 30 August 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1184 generalized continuum hypothesis], id=1184 -- WP: continuum hypothesis -- Status: M

:: Paul August ☎ 01:44, 11 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3266 Martin's axiom], id=3266 -- WP: Martin's axiom -- Status: A

:: Paul August ☎ 00:32, 11 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3270 Martin's axiom and the continuum hypothesis], id=3270 -- WP guess: Martin's axiom and the continuum hypothesis -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3893 Martin's axiom is consistent], id=3893 -- WP guess: Martin's axiom is consistent -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3221 inaccessible cardinals], id=3221 -- WP: inaccessible cardinal -- Status: A

:: Trovatore 15:02, 30 August 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3246 \clubsuit], id=3246 -- WP: clubsuit -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3245 \Diamond], id=3245 -- WP: ◊ -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5750 combinatorial principle], id=5750 -- WP guess: combinatorial principle -- Status:

::All articles processed. Paul August ☎ 05:46, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5844 neutrosophic set], id=5844 -- WP: (none) -- Status: N

::Apparently a deleted article. See also neutrosophic probability in 60A10 Probabilistic measure theory. Ben Cairns 06:07, 3 Feb 2005 (UTC).

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7187 neutrosophic set], id=7187 -- WP: none -- Status: N

::A somewhat eccentric notion of Florentin Smarandache. Paul August ☎ 05:46, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8773 fuzzy subset], id=8773^new! -- WP guess: fuzzy subset -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6339 alternative characterization of filter], id=6339 -- WP: Filter (mathematics) -- Status: A

::Paul August ☎ 04:21, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4551 class], id=4551 -- WP: class (set theory) -- Status: NM

::Paul August ☎ 04:26, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6303 comparison of filters], id=6303 -- WP: Filter (mathematics) -- Status: NM

::Paul August ☎ 04:30, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1919 complement], id=1919 -- WP: complement (set theory) -- Status: A

::Paul August ☎ 04:32, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5656 concepts in set theory], id=5656 -- WP: set (et al) -- Status: A

::Paul August ☎ 04:38, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1182 Dedekind infinite], id=1182 -- WP: Dedekind infinite -- Status: A

::Paul August ☎ 04:44, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3267 delta system], id=3267 -- WP guess: delta system -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3268 delta system lemma], id=3268 -- WP guess: delta system lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3233 diagonal intersection], id=3233 -- WP guess: diagonal intersection -- Status: C

::Article helps the understanding of Fodor's lemma and club filter, so I copied and edited it; Porcher 17:25, 1 Apr 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5659 disjoint union], id=5659 -- WP: disjoint union -- Status: NM

::In fact the MP article should replace (almost) our article. Paul August ☎ 05:03, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3259 examples of filters], id=3259 -- WP: Filter (mathematics) -- Status: NM

::Paul August ☎ 05:22, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1342 filter], id=1342 -- WP: filter (mathematics) -- Status: NM

::Paul August ☎ 05:30, Feb 13, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6302 filter basis], id=6302 -- WP: filter (mathematics) -- Status: NM

::The more common term (in my experience) is "filter base".Paul August ☎ 21:08, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1630 intersection], id=1630 -- WP: intersection (set theory) -- Status: A

::Paul August ☎ 21:14, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2090 multiset], id=2090 -- WP: multiset -- Status: NM

::Paul August ☎ 21:22, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5653 pairwise disjoint], id=5653 -- WP: pairwise disjoint -- Status: A

::Paul August ☎ 21:26, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6340 proof of alternative characterization of filter], id=6340 -- WP: filter (mathematics) -- Status: NM

::Paul August ☎ 21:30, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3269 proof of delta system lemma], id=3269 -- WP guess: proof of delta system lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=396 rational number], id=396 -- WP: rational number -- Status: A

::Paul August ☎ 21:48, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3275 saturated (set)], id=3275 -- WP guess: saturated (set) -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=1635 set], id=1635 -- WP: set -- Status: A

::Paul August ☎ 22:09, Feb 14, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2585 superset], id=2585 -- WP: subset -- Status: A

::Paul August ☎ 01:54, Feb 15, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=317 Zermelo-Fraenkel axioms], id=317 -- WP: Zermelo-Fraenkel axioms -- Status: A

::Paul August ☎ 02:00, Feb 15, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7434 basic properties of a limit along a filter], id=7434 -- WP guess: basic properties of a limit along a filter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7437 construction of Banach limit using limit along an ultrafilter], id=7437 -- WP guess: construction of Banach limit using limit along an ultrafilter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7330 equation], id=7330 -- WP: equation -- Status: A

::Paul August ☎ 02:26, 8 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7435 every bounded sequence has limit along an ultrafilter], id=7435 -- WP guess: every bounded sequence has limit along an ultrafilter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7433 limit along a filter], id=7433 -- WP guess: limit along a filter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7695 algebraic system], id=7695^new! -- WP guess: algebraic system -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8791 collection], id=8791^new! -- WP guess: collection -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8436 cumulative hierarchy], id=8436^new! -- WP guess: cumulative hierarchy -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8202 indexing set], id=8202^new! -- WP guess: indexing set -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9040 multiplicative filter], id=9040^new! -- WP guess: multiplicative filter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7853 number of ultrafilters], id=7853^new! -- WP guess: number of ultrafilters -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8906 section filter], id=8906^new! -- WP guess: section filter -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3504 \mathcal{NJ}p], id=3504 -- WP guess: \mathcalNJp -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3506 \mathcal{NK}p], id=3506 -- WP guess: \mathcalNKp -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3503 natural deduction], id=3503 -- WP: natural deduction -- Status: A

::Paul August ☎ 02:11, Feb 15, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3502 sequent], id=3502 -- WP: sequent -- Status: M

::Paul August ☎ 02:38, 21 September 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3445 sound, complete], id=3445 -- WP guess: sound, complete -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9381 Löb's theorem], id=9381^new! -- WP guess: Löb's theorem -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8174 circular reasoning], id=8174^new! -- WP guess: circular reasoning -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=4789 switching lemma], id=4789 -- WP guess: switching lemma -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3302 Elementary Functional Arithmetic], id=3302 -- WP guess: Elementary Functional Arithmetic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3301 PA], id=3301 -- WP: Peano arithmetic -- Status: A

::Paul August ☎ 19:16, 6 January 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2789 Peano arithmetic], id=2789 -- WP: Peano arithmetic -- Status: M

::Jeekc 11:50, 12 November 2005 (UTC)

::NM: 1. Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3310 ACA_0], id=3310 -- WP: Second-order arithmetic -- Status: A

:: Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3309 RCA_0], id=3309 -- WP: Second-order arithmetic -- Status: A

:: Paul August ☎ 05:10, 31 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3308 Z_2], id=3308 -- WP: Second-order arithmetic -- Status: A

:: Paul August ☎ 04:07, 31 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3307 comprehension axiom], id=3307 -- WP: Axiom schema of specification -- Status: NM

:: Paul August ☎ 21:36, 4 October 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3306 induction axiom], id=3306 -- WP: axiom of induction -- Status: C

::The axiom of induction (or induction axiom) in its various forms is described in WP in several places: Peano axioms, second-order arithmetic, Kripke–Platek set theory, number system, but it should have its own article.

• PM: [http://planetmath.org/?op=getobj&from=objects&id=5931 inhabited set], id=5931 -- WP: inhabited set -- Status: A

:: Paul August ☎ 03:56, 31 May 2006 (UTC)

::NC: 1. Mathemens (talk) 22:46, 30 April 2008 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6248 computable real function], id=6248 -- WP: computable real function -- Status: C

:: Mathemens (talk) 22:46, 30 April 2008 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=6247 computable sequence], id=6247 -- WP : computable sequence -- Status: NC

:: Paul August ☎ 20:42, 29 May 2006 (UTC)

:: All articles processed. Paul August ☎ 05:37, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2602 Boolean ring], id=2602 -- WP: Boolean ring -- Status: A

::CryptoDerk 15:56, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3983 M. H. Stone's representation theorem], id=3983 -- WP: Stone's representation theorem for Boolean algebras -- Status: A

:: Paul August ☎ 05:37, 28 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9319 Boolean ideal], id=9319^new! -- WP guess: Boolean ideal -- Status:

::All articles processed. Paul August ☎ 20:43, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2594 Boolean lattice], id=2594 -- WP: Boolean algebra -- Status: A

::CryptoDerk 15:52, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3304 complete lattice], id=3304 -- WP: complete lattice -- Status: A

::CryptoDerk 15:51, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=2593 lattice], id=2593 -- WP: lattice (order) -- Status: A

::CryptoDerk 15:50, Apr 30, 2005 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9303 bounded complete], id=9303^new! -- WP guess: bounded complete -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8832 criteria for a poset to be a complete lattice], id=8832^new! -- WP guess: criteria for a poset to be a complete lattice -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8238 De Morgan algebra], id=8238^new! -- WP guess: De Morgan algebra -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9406 intersection structure], id=9406^new! -- WP guess: intersection structure -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8943 commutativity relation in an orthocomplemented lattice], id=8943^new! -- WP guess: commutativity relation in an orthocomplemented lattice -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=7822 orthocomplemented lattice], id=7822^new! -- WP guess: orthocomplemented lattice -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8735 orthomodular lattice], id=8735^new! -- WP guess: orthomodular lattice -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=9056 quantum logic], id=9056^new! -- WP guess: quantum logic -- Status:

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8796 topos], id=8796^new! -- WP guess: topos -- Status:

::NM: 4. Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3496 biextensional collapse], id=3496 -- WP guess: Chu Space -- Status: NM

:: Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3495 Chu space], id=3495 -- WP: Chu space -- Status: NM

:: Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3499 Chu transform], id=3499 -- WP: Chu space -- Status: NM

:: Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3498 example of Chu space], id=3498 -- WP: Chu space -- Status: NM

:: Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=3497 property of a Chu space], id=3497 -- WP guess: Chu space -- Status: NM

:: Paul August ☎ 20:24, 29 May 2006 (UTC)

• PM: [http://planetmath.org/?op=getobj&from=objects&id=8638 non-standard analysis], id=8638^new! -- WP guess: non-standard analysis -- Status: