Set Theory

In 1874 Cantor published an article in Crelle 's Journal which marks the birth of set theory

In set theory, Kőnig's theorem states that if the axiom of choice holds

is a thought experiment which illustrates a counterintuitive property of infinite sets

In constructive set theory, Myhill proposed an axiom system that avoids the axiom of choice and the law of the excluded middle, known as intuitionistic Zermelo-Fraenkel.

His research interests include set theory and combinatorics.

In the last eight years of his life Kőnig's interests turned towards set theory and he contributed to the continuum hypothesis.

Tennenbaum proved the relative consistency of the negation of Suslin's hypothesis by applying an early version of forcing

Ernst Schröder was a German mathematician who did important work is in the area of algebra, set theory and logic.

Mirimanoff made notable contributions to axiomatic set theory and to number theory

He was particularly drawn to Georg Cantor's set theory.

seminal contributions to automata theory, modal logic, set theory

contributed early developments to axiomatic set theory (ZFC)

his book on set theory became a standard introduction to the field

He performed research in the field of set theory and predicate logic.

is an American mathematician at Harvard University specializing in set theory.

known for his work on set theory

indeed a vital result in the development of set theory

She has been dedicated to understanding and explaining the methods that set theorists use in agreeing on axioms, especially those that go beyond ZFC.

The theory of sets and transfinite arithmetic

In set theory, a Woodin cardinal (named for W.

In descriptive set theory, the Borel determinacy theorem states that any Gale-Stewart game whose payoff set is a Borel set is dete

In mathematics, particularly in set theory, the beth numbers form a certain (unset) sequence of infinite cardinal numbers (also kn

In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend e

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is th

In set theory, an Aronszajn tree is a tree of uncountable height with no uncountable branches and no uncountable levels.

In set theory, a cardinal number is a strongly inaccessible cardinal if it is uncountable, regular, and a strong limit cardinal.

In mathematics, specifically in set theory, a measurable cardinal is a certain kind of large cardinal number.

In mathematics, particularly in set theory, Fodor's lemma (or the pressing-down lemma) states: In modern parlance, the nonstationa

In the mathematical field of set theory, the Solovay model is a model constructed by Robert M.

In set theory, Easton's theorem is a result on the possible cardinal numbers of powersets.

In axiomatic set theory and the branches of mathematics and philosophy that use it, the axiom of infinity is one of the axioms of

set theory

is an American set theorist

known for contributions to set theory

his thesis was titled Ensembles ordonnés et ramifiés

Robert Martin Solovay (born December 15, 1938) is an American mathematician working in set theory.

He is primarily known for his contributions to set theory, topology, measure theory and graph theory.

Shoenfield worked on recursion theory, model theory and axiomatic set theory.

Much of his most influential work was on Willard Van Orman Quine's New Foundations, a set theory with a universal set, but he is most famous for the Kochen-Specker theorem in quantum mechanics, showing that certain types of hidden-variable theories are impossible.

However, this equivalence is not valid in constructive or intuitionistic logic, and so this separate terminology is mostly used in the set theory of constructive mathematics.

Any pairing function can be used in set theory to prove that integers and rational numbers have the same cardinality as natural numbers.

That is, set theory serves as foundation of mathematics.

In the modern foundations of mathematics, and, typically, in set theory, a function is actually equal to its graph.

Foundations of Mathematics Set Theory

Foundations of Mathematics Set Theory

Foundations of Mathematics Set Theory

Foundations of Mathematics Set Theory

Foundations of Mathematics Set Theory

Foundations of Mathematics Set Theory

In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects

well-ordered set

The absolute infinite is an extension of the idea of infinity proposed by mathematician Georg Cantor. Cantor

In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that

In mathematics, a surjective function (also known as surjection, or onto function ) is a function f such that

In mathematics, an uncountable set, informally, is an infinite set that contains

In mathematics, injections, surjections, and bijections are classes of functions distinguished by the

equivalent to the Axiom of Choice

Abraham Fraenkel was a German-born mathematician who made contributions to axiomatic set theory. He is the F in the ZFC axioms for set theory.