• Set theory
  • Axiomatic set theory
  • Naive set theory
  • Zermelo set theory
  • Zermelo-Fraenkel set theory
  • Kripke-Platek set theory with urelements
• Simple theorems in the algebra of sets
• Axiom of choice
  • Zorn's lemma
• Empty set
• Cardinality
  • Cardinal number
  • Aleph number
    • Aleph null
    • Aleph one
  • Beth number
• Ordinal number
  • Well-order
  • Limit ordinal
  • Successor ordinal
  • Transfinite induction
  • Well-founded set
  • Infinite descending chain
• Set
• Algebra of sets
• Countable set
• Cantor's diagonal argument
• Cantor's first uncountability proof
• Cantor's theorem
• Cantor-Bernstein-Schroeder theorem
• Continuum hypothesis
  • Forcing (mathematics)
• Cantor's back-and-forth method
• Class (set theory)
• Internal set theory
• Fuzzy set
• Union (set theory)
• Intersection (set theory)
• Complement (set theory)
• Cartesian product
• Subset
• Power set
• Russell's paradox
• Burali-Forti paradox
• Tree (set theory)
• Tree (descriptive set theory)
• Continuum (mathematics)
  • Suslin's problem
• Musical set theory
• Descriptive set theory
  • Polish space
  • Borel equivalence relation
  • Analytical hierarchy
  • Prewellordering
  • Uniformization (set theory)
  • Analytic set
  • Projective set
  • Property of Baire
  • Perfect set property

Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In the branch of mathematics known as set theory, aleph usually refers to a series of numbers used to represent the cardinality (or size) of infinite sets. ... In mathematics, the Hebrew letter (aleph) with various subscripts represents various infinite cardinal numbers (see aleph number). ... Commonly, ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. ... When defining the ordinal numbers, an absolutely fundamental operation that we can perform on them is a successor operation S to get the next higher one. ... Transfinite induction is the proof technique of mathematical induction when applied to (large) well-ordered sets, for instance to sets of ordinals or cardinals, or even to the class of all ordinals. ... Given a set S with a partial order <=, an infinite descending chain is a Chain V, that is, a subset of S upon which <= defines a total order, such that V has no minimal element, that is, an element m such that for all elements n in V it holds... In mathematics, a set can be thought of as any well-defined collection of things considered as a whole. ... In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. ... Fuzzy sets are an extension of the classical set theory used in Fuzzy logic. ... In set theory and other branches of mathematics, two kinds of complements are defined, the relative complement and the absolute complement. ... In mathematics, the Cartesian product (or direct product) X Y of two sets X and Y is the set of all possible ordered pairs whose first component is a member of X and whose second component is a member of Y. This concept is named after Ren Descartes. ... In mathematics, the word continuum sometimes denotes the real line. ... Suslins problem in mathematics is a question about orders posed by M. Suslin in the early 1920s. ... Musical set theory is a atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... This is a glossary of some terms used in the branch of mathematics known as topology. ... In mathematical logic and descriptive set theory, the analytical hierarchy is a second-order analogue of the arithmetical hierarchy. ... In descriptive set theory, a subset of a Polish space has the perfect set property if it is either countable or has a nonempty perfect subset. ...

Set theorists

• Georg Cantor
• Paul Cohen
• Abraham Fraenkel
• Kurt Gödel
• Alexander S. Kechris
• Donald A. Martin
• Yiannis N. Moschovakis
• John von Neumann
• Thoralf Skolem
• John R. Steel
• W. Hugh Woodin
• Ernst Zermelo

Georg Cantor Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845 – January 6, 1918) was a mathematician who was born in Russia and lived in Germany for most of his life. ... Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... Donald A. (Tony) Martin is a set theorist and philosopher of mathematics at UCLA. Among his most notable work are the proofs of Borel determinacy (from ZFC alone), the proof (with John R. Steel) of projective determinacy (from suitable large cardinal axioms), and his work on Martins axiom. ... Yiannis N. Moschovakis is a set theorist, descriptive set theorist, and recursion (computability) theorist, at UCLA. For many years he has split his time between UCLA and University of Athens (he is retiring from the latter in July, 2005). ... John von Neumann in the 1940s. ... John R. Steel is a set theorist at University of California, Berkeley (formerly at UCLA). ... W. Hugh Woodin is a set theorist at University of California, Berkeley. ... Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician and philosopher. ...

Societies and organizations

• Association for Symbolic Logic
• The Cabal