Bounds on maximal number of transversals in a Latin square A transversal in a Latin square of order n is a set S of n cells such that every row and every column contains exactly one cell of S, and suc ...
In the field of mathematics known as functional analysis, the invariant subspace problem for a complex Banach space H of dimension 1 is the question whether every bounded linear operator T : H → H h ...
In set theory, a regular cardinal is a cardinal number that is equal to its own cofinality. So, crudely speaking, a regular cardinal is one which cannot be broken into a smaller collection of smaller ...
In set theory, a branch of mathematics, a Reinhardt cardinal is a large cardinal κ, suggested by William Nelson Reinhardt (1967, 1974), that is the critical point of a non-trivial elementary embeddin ...
A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f(s) is an element of s. With this concept, the axiom can be stated:For any set X of none ...
In set theory, a Jónsson cardinal (named after Bjarni Jónsson) is a certain kind of large cardinal number.An uncountable cardinal number κ is said to be Jónsson if for every function f: ω → κ t ...
The generalized continuum hypothesis (GCH) states that if an infinite set's cardinality lies between that of an infinite set S and that of the power set of S, then it either has the same cardinality a ...
If λ is any ordinal, κ is λ-supercompact means that there exists an elementary embedding j from the universe V into a transitive inner model M with critical point κ, j(κ)λ and{ }^\lambda M\subse ...
In mathematical set theory, a strongly compact cardinal is a certain kind of large cardinal number.A cardinal κ is strongly compact if and only if every κ-complete filter can be extended to a κ com ...
In theories of arithmetic, such as Peano arithmetic, there is an intricate relationship between the consistency of the theory and its completeness. A theory is complete if, for every formula φ in its ...
In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structu ...
Born in Tucson, Arizona, Woodin earned his Ph.D. from the University of California, Berkeley in 1984 under Robert M. Solovay. His dissertation title was Discontinuous Homomorphisms of C(Omega) and Set ...
If A is an infinite set of regular cardinals, D is an ultrafilter on A, then we let cf(\prod A/D) denote the cofinality of the ordered set of functions \prod A where the ordering is defined as follows ...
Shelah was born in Jerusalem on July 3, 1945. He is the son of the Israeli poet and political activist Yonatan Ratosh. He received his PhD in 1969 from the Hebrew University.Shelah is married to Yael, ...
In set theory, the singular cardinals hypothesis (SCH) arose from the question of whether the least cardinal number for which the generalized continuum hypothesis (GCH) might fail could be a singular ...
