Moti Gitik

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.

• Gitik, Moti (1986). "Changing Cofinalities and the Nonstationary Ideal". Israel Journal of Mathematics. 56 (3): 280–314. doi:10.1007/BF02782938.
• Gitik, Moti (1991). "The strength of the failure of the singular cardinal hypothesis". Annals of Pure and Applied Logic. 51 (3): 215–240. doi:10.1016/0168-0072(91)90016-F.
• Gitik, Moti; Magidor, Menachem (1992). "The Singular Cardinal Hypothesis revisited". MSRI Publications. Mathematical Sciences Research Institute Publications. 26: 243–279. doi:10.1007/978-1-4613-9754-0_16. ISBN 978-1-4613-9756-4.
• Gitik, Moti (1996). "Blowing up the power of a singular cardinal". Annals of Pure and Applied Logic. 80 (1): 17–33. doi:10.1016/0168-0072(95)00046-1.
• Gitik, Moti (2020). "Extender based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis". Journal of Mathematical Logic. 20 (3): 2050013. doi:10.1142/S0219061320500130. S2CID 46948714.

• Moti Gitik at the Mathematics Genealogy Project