Keywords

#compactness_theorem

Compactness theorem

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 constructing models of any set of sentences that is finitely consistent.

Fri 19th

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Compactness theorem Tychonoff's theorem Gödel's completeness theorem Compact space Bolzano–Weierstrass theorem Mahler's compactness theorem Rellich–Kondrachov theorem Gromov's compactness theorem Model theory Löwenheim–Skolem theorem
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