PlanetMath: syntactic compactness theorem for first order logic

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syntactic compactness theorem for first order logic

(Theorem)

Let $L$ be a first-order language, and $\Delta\subseteq L$ be a set of sentences. If $\Delta$ is inconsistent, then some finite $\Gamma\subseteq\Delta$ is inconsistent.

"syntactic compactness theorem for first order logic" is owned by jihemme.

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Attachments:: proof of compactness theorem for first order logic (Proof) by CWoo
criterion for consistency of sets of formulas (Corollary) by jihemme
creating an infinite model (Example) by CWoo

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Cross-references: finite, inconsistent, sentences, first-order language
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This is version 2 of syntactic compactness theorem for first order logic, born on 2002-06-04, modified 2002-06-09.
Object id is 3033, canonical name is CompactnessTheoremForFirstOrderLogic.
Accessed 3899 times total.

Classification:

AMS MSC:	03B10 (Mathematical logic and foundations :: General logic :: Classical first-order logic)
	03C07 (Mathematical logic and foundations :: Model theory :: Basic properties of first-order languages and structures)

Pending Errata and Addenda

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