cointerpretability
In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of T. The "translation" here is required to preserve the logical structure of formulas.
This concept, in a sense dual to interpretability, was introduced by {{harvtxt|Japaridze|1993}}, who also proved that, for theories of Peano arithmetic and any stronger theories with effective axiomatizations, cointerpretability is equivalent to -conservativity.
See also
References
- {{citation
| last = Japaridze| first = Giorgi | authorlink = Giorgi Japaridze
| doi = 10.1016/0168-0072(93)90201-N
| issue = 1–2
| journal = Annals of Pure and Applied Logic
| mr = 1218658
| pages = 113–160
| title = A generalized notion of weak interpretability and the corresponding modal logic
| volume = 61
| year = 1993| doi-access =
}}.
- {{citation
| last1 = Japaridze | first1 = Giorgi | author1-link = Giorgi Japaridze
| last2 = de Jongh | first2 = Dick | author2-link = Dick de Jongh
| editor-last = Buss | editor-first = Samuel R. | editor-link = Samuel Buss
| contribution = The logic of provability
| doi = 10.1016/S0049-237X(98)80022-0
| location = Amsterdam
| mr = 1640331
| pages = 475–546
| publisher = North-Holland
| series = Studies in Logic and the Foundations of Mathematics
| title = Handbook of Proof Theory
| volume = 137
| year = 1998| doi-access = free
}}.
Category:Mathematical relations
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