Moti Gitik () is a mathematician, working in

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

, who is professor at the

Tel-Aviv University Tel Aviv University (TAU) ( he, אוּנִיבֶרְסִיטַת תֵּל אָבִיב, ''Universitat Tel Aviv'') is a public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Loc ...

. He was an invited speaker at the 2002 International Congresses of Mathematicians, and became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2012.List of Fellows of the American Mathematical Society
retrieved 2013-01-19.

Research

Gitik proved the

consistency In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent ...

of "all uncountable cardinals are

singular Singular may refer to: * Singular, the grammatical number that denotes a unit quantity, as opposed to the plural and other forms * Singular homology * SINGULAR, an open source Computer Algebra System (CAS) * Singular or sounder, a group of boar, ...

" (a strong negation of the

axiom of choice In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that ''a Cartesian product of a collection of non-empty sets is non-empty''. Informally put, the axiom of choice says that given any collectio ...

) from the consistency of "there is a proper class of strongly compact cardinals". He further proved the

equiconsistency In mathematical logic, two theory (mathematical logic), theories are equiconsistent if the consistency of one theory implies the consistency of the other theory, and Vice-versa, vice versa. In this case, they are, roughly speaking, "as consistent ...

of the following statements: * There is a cardinal ''κ'' with

Mitchell order In mathematical set theory, the Mitchell order is a well-founded preorder on the set of normal measures on a measurable cardinal ''κ''. It is named for William Mitchell. We say that ''M'' ◅ ''N'' (this is a strict order) if ''M'' is in the ultr ...

''κ''⁺⁺. * There is a

measurable cardinal In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal , or more generally on any set. For a cardinal , it can be described as a subdivisio ...

''κ'' with 2^''κ'' > ''κ''⁺. * There is a strong limit

singular cardinal Singular may refer to: * Singular, the grammatical number that denotes a unit quantity, as opposed to the plural and other forms * Singular homology * SINGULAR, an open source Computer Algebra System (CAS) * Singular or sounder, a group of boar, s ...

''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

* * * * *

References

{{DEFAULTSORT:Gitik, Moti Living people Tel Aviv University faculty Fellows of the American Mathematical Society 20th-century Israeli mathematicians 21st-century Israeli mathematicians Set theorists Year of birth missing (living people)

Research

Selected publications

See also

References