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...

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...

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

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

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

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

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...

In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician...

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

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

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)...

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

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...

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...

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

Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian) is a result that relates three different kinds of weak compactness in...

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

theory) Barbier's theorem (geometry) Bapat–Beg theorem (statistics) Baranyai's theorem (combinatorics) Barwise compactness theorem (mathematical logic)...

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

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

\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...

Gromov's compactness theorem (geometry) – On when a set of compact Riemannian manifolds of a given dimension is relatively compact Ambrose, W. A theorem of...

infinite subsets of the domain. It follows from the compactness theorem and the upward Löwenheim–Skolem theorem that it is not possible to characterize finiteness...

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

fundamental compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem is automatically...

noncollapsing theorem is that volume control is one of the preconditions of Hamilton's compactness theorem. As a consequence, Hamilton's compactness and the...

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...

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

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...