Moti Gitik () is a mathematician, working in

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), 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 mathema ...

, who is professor at the

Tel-Aviv University Tel Aviv University (TAU) is a Public university, public research university in Tel Aviv, Israel. With over 30,000 students, it is the largest university in the country. Located in northwest Tel Aviv, the university is the center of teaching and ...

. 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 deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences ...

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 or sounder, a group of boar, see List of animal names * Singular (band), a Thai jazz pop duo *'' Singula ...

" (a strong negation of the

axiom of choice In mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of non-empty sets, it is possible to construct a new set by choosing one element from e ...

) from the consistency of "there is a proper class of

strongly compact cardinal In set theory, a strongly compact cardinal is a certain kind of large cardinal. An uncountable cardinal κ is strongly compact if and only if every κ-complete filter can be extended to a κ-complete ultrafilter. Strongly compact cardinals were ...

s". 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 ''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 (mathematics), measure on a cardinal ''κ'', or more generally on any set. For a cardinal ''κ'', ...

''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 or sounder, a group of boar, see List of animal names * Singular (band), a Thai jazz pop duo *'' Singular ...

''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

External links

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