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...

selection theorem, following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the...

topological spaces based on fuzzy sets. The theorem depends crucially upon the precise definitions of compactness and of the product topology; in fact, Tychonoff's...

compact if and only if it is closed and bounded. The theorem is sometimes called the sequential compactness theorem. The Bolzano–Weierstrass theorem is...

Gromov's compactness theorem can refer to either of two mathematical theorems: Gromov's compactness theorem (geometry) stating that certain sets of Riemannian...

Löwenheim–Skolem theorem is one of the two key properties, along with the compactness theorem, that are used in Lindström's theorem to characterize first-order...

then Tennenbaum's theorem shows that it has no recursive non-standard models. The completeness theorem and the compactness theorem are two cornerstones...

topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space...

Gromov's theorem may mean one of a number of results of Mikhail Gromov: One of Gromov's compactness theorems: Gromov's compactness theorem (geometry)...

to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization...

that both the completeness and compactness theorems were implicit in Skolem 1923...." [Dawson, J. W. (1993). "The compactness of first-order logic:from Gödel...

as well. Bolzano–Weierstrass theorem Raman-Sundström, Manya (August–September 2015). "A Pedagogical History of Compactness". American Mathematical Monthly...

equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis and various results concerning compactness of integral operators...

selection theorem, since one "selects" a convergent subsequence. (However, today the customary name is "compactness theorem", whereas "selection theorem" has...

include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization...

This theorem is also called the Banach–Alaoglu theorem or the weak-* compactness theorem and it is commonly called simply the Alaoglu theorem. If X {\displaystyle...

mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theorem for first-order logic to a...

test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X. Some major theorems characterize...

models of arithmetic can be demonstrated by an application of the compactness theorem. To do this, a set of axioms P* is defined in a language including...

\kappa } -compact. (W. W. Comfort, S. Negrepontis, The Theory of Ultrafilters, p.185) A language Lκ,κ is said to satisfy the weak compactness theorem if whenever...

his axiomatisation, Henkin proved that Gödel's completeness theorem and compactness theorem, which hold for first-order logic, carry over to second-order...

In the mathematical field of symplectic topology, Gromov's compactness theorem states that a sequence of pseudoholomorphic curves in an almost complex...

Ax–Grothendieck theorem (model theory) Barwise compactness theorem (mathematical logic) Borel determinacy theorem (set theory) Büchi-Elgot-Trakhtenbrot theorem (mathematical...

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...

admits a convergent subsequence. In other words, it is a sequential compactness theorem for the space of uniformly bounded monotone functions. It is named...

In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures...

subsequence. The Delta-compactness theorem is similar to the Banach–Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem (in the non-separable...

differential geometry and in particular Yang–Mills theory, Uhlenbeck's compactness theorem is a result about sequences of (weak Yang–Mills) connections with...

Lindström's theorem implies that the only extension of first-order logic satisfying both the compactness theorem and the downward Löwenheim–Skolem theorem is first-order...

Gromov's compactness theorem, stating that the set of compact Riemannian manifolds with Ricci curvature ≥ c and diameter ≤ D is relatively compact in the...