Moti Gitik
Encyclopedia
Moti Gitik is a mathematician, working in set theory
. Gitik is professor at the Tel-Aviv University. He proved the consistency of "all uncountable cardinals are singular" (a statement that negates the axiom of choice) from the consistency of "there is a proper class of strongly compact cardinal
s". He further proved the equiconsistency
of the following statements:
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
. Gitik is professor at the Tel-Aviv University. He proved the consistency of "all uncountable cardinals are singular" (a statement that negates the axiom of choice) from the consistency of "there is a proper class of strongly compact cardinal
Strongly compact cardinal
In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number; their existence can neither be proven nor disproven from the standard axioms of set theory....
s". He further proved the equiconsistency
Equiconsistency
In mathematical logic, two theories are equiconsistent if, roughly speaking, they are "as consistent as each other".It is not in general possible to prove the absolute consistency of a theory T...
of the following statements:
- There is a cardinal κ with Mitchell orderMitchell orderIn 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 if M is in the ultrapower model defined by N...
κ++. - There is a measurable cardinalMeasurable cardinal- Measurable :Formally, a measurable cardinal is an uncountable cardinal number κ such that there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ...
κ with 2κ > κ+. - There is a strong limit singular cardinal λ with 2λ > λ+.
- The GCHContinuum hypothesisIn mathematics, the continuum hypothesis is a hypothesis, advanced by Georg Cantor in 1874, about the possible sizes of infinite sets. It states:Establishing the truth or falsehood of the continuum hypothesis is the first of Hilbert's 23 problems presented in the year 1900...
holds below ℵω and 2ℵω=ℵω+2.
External links
- Gitik's homepage, at Tel Aviv UniversityTel Aviv UniversityTel Aviv University is a public university located in Ramat Aviv, Tel Aviv, Israel. With nearly 30,000 students, TAU is Israel's largest university.-History:...