Moti Gitik
{{short description|Israeli mathematician}}
{{BLP sources|date=January 2013}}
{{Infobox scientist
| name = Moti Gitik
| native_name = מוטי גיטיק
| native_name_lang = he
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| thesis_title = All Uncountable Cardinals can be Singular
| thesis_year = 1980
| fields = Set theory
| workplaces = Tel Aviv University
| alma_mater = Hebrew University of Jerusalem
| doctoral_advisors = Azriel Levy
Menachem Magidor
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| awards = Karp Prize (2013)
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| website = {{url|http://www.math.tau.ac.il/~gitik/|math.tau.ac.il/~gitik/}}
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Moti Gitik ({{Langx|he|מוטי גיטיק}}) is a mathematician, working in set theory, who is professor at the Tel-Aviv University. He was an invited speaker at the 2002 International Congresses of Mathematicians, and became a fellow of the American Mathematical Society in 2012.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-19.
Research
Gitik proved the consistency of "all uncountable cardinals are singular" (a strong negation of the axiom of choice) from the consistency of "there is a proper class of strongly compact cardinals". He further proved the equiconsistency of the following statements:
- There is a cardinal κ with Mitchell order κ++.
- There is a measurable cardinal κ with 2κ > κ+.
- There is a strong limit singular cardinal λ with 2λ > λ+.
- The GCH holds below ℵω, and 2ℵω=ℵω+2.
Gitik discovered several methods for building models of ZFC with complicated Cardinal Arithmetic structure. His main results deal with consistency and equi-consistency of non-trivial patterns of the Power Function over singular cardinals.
Selected publications
- {{cite journal
| last1=Gitik | first1=Moti
| title=Changing Cofinalities and the Nonstationary Ideal
| journal=Israel Journal of Mathematics
| volume=56
| issue=3
| pages=280–314
| date=1986
| doi=10.1007/BF02782938 | doi-access=free}}
- {{cite journal
| last1=Gitik | first1=Moti
| title=The strength of the failure of the singular cardinal hypothesis
| journal=Annals of Pure and Applied Logic
| volume=51
| issue=3
| date=1991
| pages=215–240
| doi=10.1016/0168-0072(91)90016-F | doi-access=free}}
- {{cite book
| last1=Gitik | first1=Moti
| last2=Magidor | first2=Menachem
| chapter=The Singular Cardinal Hypothesis Revisited
| title=Set Theory of the Continuum
| journal=MSRI Publications
| series=Mathematical Sciences Research Institute Publications
| volume=26
| date=1992
| pages=243–279
| doi=10.1007/978-1-4613-9754-0_16 | isbn=978-1-4613-9756-4
| doi-access=free}}
- {{cite journal
| last1=Gitik | first1=Moti
| title=Blowing up the power of a singular cardinal
| journal=Annals of Pure and Applied Logic
| volume=80
| issue=1
| date=1996
| pages=17–33
| doi=10.1016/0168-0072(95)00046-1 | doi-access=free| arxiv=math/9404204
}}
- {{cite journal
| last1=Gitik | first1=Moti
| title=Extender based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis
| journal=Journal of Mathematical Logic
| volume=20
| issue=3
| date=2020
| pages=2050013
| doi=10.1142/S0219061320500130| s2cid=46948714
}}
References
{{Reflist}}
External links
- {{MathGenealogy|id=7699}}
{{Authority control}}
{{DEFAULTSORT:Gitik, Moti}}
Category:Academic staff of Tel Aviv University
Category:Fellows of the American Mathematical Society
Category:20th-century Israeli mathematicians