﻿

# compactness theorem

Theorem stating that any collection of well-formed formulae of a language has a model, if every finite subset of the collection has a model.

Philosophy dictionary. . 2011.

### Look at other dictionaries:

• 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

• Mahler's compactness theorem — In mathematics, Mahler s compactness theorem, proved by Kurt Mahler (1946), is a foundational result on lattices in Euclidean space, characterising sets of lattices that are bounded in a certain definite sense. Looked at another way, it… …   Wikipedia

• Mumford's compactness theorem — In mathematics, Mumford s compactness theorem states that the space of compact Riemann surfaces of fixed genus g > 1 with no closed geodesics of length less than some fixed ε > 0 in the Poincaré metric is compact. It was …   Wikipedia

• Barwise compactness theorem — In mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theorem for first order logic to a certain class of infinitary languages. It was stated and proved by Barwise in… …   Wikipedia

• Gromov's compactness theorem — can refer to either of two mathematical theorems:* Gromov s compactness theorem (geometry) in Riemannian geometry * Gromov s compactness theorem (topology) in symplectic topology …   Wikipedia

• Gromov's compactness theorem (topology) — For Gromov s compactness theorem in Riemannian geometry, see that article. In symplectic topology, Gromov s compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex manifold with a uniform energy bound must have …   Wikipedia

• Gromov's compactness theorem (geometry) — For Gromov s compactness theorem in symplectic topology, see that article. In Riemannian geometry, Gromov s (pre)compactness theorem states that the set of Riemannian manifolds of a given dimension, with Ricci curvature ≥ c and diameter ≤ D is… …   Wikipedia

• compactness — See compactly. * * * ▪ mathematics       in mathematics, property of some topological spaces (a generalization of Euclidean space) that has its main use in the study of functions defined on such spaces. An open covering of a space (or set) is a… …   Universalium

• 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

• 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