Moti Gitik

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Moti Gitik (Hebrew: 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.^[1]

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 2^κ > κ⁺.
• There is a strong limit singular cardinal λ with 2^λ > λ⁺.
• The GCH holds below ℵ_ω, and 2^ℵ_ω=ℵ_ω+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[]

• Moti Gitik, "Changing Cofinalities and the Nonstationary Ideal", Israel Journal of Math 56, 3, (1986).
• Moti Gitik, "The strength of the failure of the singular cardinal hypothesis", Ann. of Pure and Appl. Logic 51 (1991), 215-240.
• Moti Gitik, Menachem Magidor, " The Singular Cardinal Hypothesis revisited", MSRI Publications 26 (1992), 243-279.
• Moti Gitik, "Blowing up the power of a singular cardinal", Ann. of Pure and Applied Logic 80 (1996), 17-33.
• Moti Gitik, "Extender based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis", J. Math. Logic 20(3), 2020, 2050013. 

See also[]

• Moti Gitik at the Mathematics Genealogy Project

References[]