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Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects … Wikipedia
Class (set theory) — In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) which can be unambiguously defined by a property that all its members share. The precise definition of class… … Wikipedia
Zermelo set theory — Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. It bears certain differences from its descendants, which are not always understood, and are frequently misquoted. This article… … Wikipedia
Implementation of mathematics in set theory — This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine s New… … Wikipedia
Rank — is a very broad term with several meanings. As a noun it is usually related to a relative position or to some kind of ordering (see also ranking). As an adjective it is used to mean profuse, conspicuous, absolute, or unpleasant, especially in… … Wikipedia
Morse–Kelley set theory — In the foundation of mathematics, Morse–Kelley set theory (MK) or Kelley–Morse set theory (KM) is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG). While von Neumann–Bernays–Gödel set theory … Wikipedia
Rank (mathematics) — Rank means a wide variety of things in mathematics, including: * Rank (linear algebra) * Rank of a tensor * Rank of an abelian group * Rank of a Lie group * Percentile rank * Rank (differential topology) * Rank of a vector bundle * Rank (set… … Wikipedia
Rank-into-rank — In set theory, a branch of mathematics, a rank into rank is a large cardinal lambda; satisfying one of the following four axioms (commonly known as rank into rank embeddings, given in order of increasing consistency strength):*Axiom I3: There is… … Wikipedia
Theory of Deep Democracy — Theory of Deep DemocracyThe theory of deep democracy makes a distinction between merely formal and deeper forms of democracy. Formal democracy is an important part of deep democracy, but it is merely a beginning or a necessary condition. In order … Wikipedia
Rank of a group — For the dimension of the Cartan subgroup, see Rank of a Lie group In the mathematical subject of group theory, the rank of a group G , denoted rank( G ), can refer to the smallest cardinality of a generating set for G , that is:… … Wikipedia
