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cardinality theorem

См. также в других словарях:

  • Cardinality of the continuum — In mathematics, the cardinality of the continuum, sometimes also called the power of the continuum, is the size (cardinality) of the set of real numbers mathbb R (sometimes called the continuum). The cardinality of mathbb R is often denoted by… …   Wikipedia

  • Cardinality — In mathematics, the cardinality of a set is a measure of the number of elements of the set . For example, the set A = {1, 2, 3} contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality ndash; one which… …   Wikipedia

  • Dimension theorem for vector spaces — In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space.… …   Wikipedia

  • Dilworth's theorem — In mathematics, in the areas of order theory and combinatorics, Dilworth s theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician …   Wikipedia

  • König's theorem (set theory) — For other uses, see König s theorem. In set theory, König s theorem (named after the Hungarian mathematician Gyula König) colloquially states that if the axiom of choice holds, I is a set, mi and ni are cardinal numbers for every i in I , and m i …   Wikipedia

  • Cantor's theorem — Note: in order to fully understand this article you may want to refer to the set theory portion of the table of mathematical symbols. In elementary set theory, Cantor s theorem states that, for any set A , the set of all subsets of A (the power… …   Wikipedia

  • Löwenheim–Skolem theorem — In mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ. The… …   Wikipedia

  • Morley's categoricity theorem — Vaught s test redirects here. Not to be confused with the Tarski–Vaught test. Categorical theory redirects here. Not to be confused with Category Theory. In model theory, a branch of mathematical logic, a theory is κ categorical (or categorical… …   Wikipedia

  • De Bruijn–Erdős theorem (graph theory) — This article is about coloring infinite graphs. For the number of lines determined by a finite set of points, see De Bruijn–Erdős theorem (incidence geometry). In graph theory, the De Bruijn–Erdős theorem, proved by Nicolaas Govert de Bruijn and… …   Wikipedia

  • Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia

  • Compactness theorem — In mathematical logic, the compactness theorem states that a set of first order sentences has a model if and only if every finite subset of it has a model. This theorem is an important tool in model theory, as it provides a useful method for… …   Wikipedia

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