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...
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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...
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then Tennenbaum's theorem shows that it has no recursive non-standard models. The completeness theorem and the compactness theorem are two cornerstones...
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compact if and only if it is closed and bounded. The theorem is sometimes called the sequential compactness theorem. The Bolzano–Weierstrass theorem is...
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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...
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Gromov's compactness theorem can refer to either of two mathematical theorems: Gromov's compactness theorem (geometry) stating that certain sets of Riemannian...
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selection theorem, following an older convention used in naming compactness theorems, because they were formulated in terms of sequential compactness (the...
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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...
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In mathematics, the Rellich–Kondrachov theorem is a compact embedding theorem concerning Sobolev spaces. It is named after the Austrian-German mathematician...
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that both the completeness and compactness theorems were implicit in Skolem 1923...." [Dawson, J. W. (1993). "The compactness of first-order logic:from Gödel...
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First-order logic (section The compactness theorem)
to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem. First-order logic is the standard for the formalization...
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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)...
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equations, Montel's theorem in complex analysis, and the Peter–Weyl theorem in harmonic analysis and various results concerning compactness of integral operators...
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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...
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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...
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admits a convergent subsequence. In other words, it is a sequential compactness theorem for the space of uniformly bounded monotone functions. It is named...
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Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian) is a result that relates three different kinds of weak compactness in...
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as well. Bolzano–Weierstrass theorem Raman-Sundström, Manya (August–September 2015). "A Pedagogical History of Compactness". American Mathematical Monthly...
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theory) Barbier's theorem (geometry) Bapat–Beg theorem (statistics) Baranyai's theorem (combinatorics) Barwise compactness theorem (mathematical logic)...
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Gromov's compactness theorem, stating that the set of compact Riemannian manifolds with Ricci curvature ≥ c and diameter ≤ D is relatively compact in the...
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test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X. Some major theorems characterize...
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\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...
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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...
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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...
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Ultraproduct (redirect from Los's theorem)
include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization...
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fundamental compactness theorem for sequences of metric spaces. In the special case of Riemannian manifolds, the key assumption of his compactness theorem is automatically...
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noncollapsing theorem is that volume control is one of the preconditions of Hamilton's compactness theorem. As a consequence, Hamilton's compactness and the...
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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...
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mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theorem for first-order logic to a...
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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...
68 KB (8,331 words) - 12:56, 25 July 2024