PlanetMath: criterion for consistency of sets of formulas

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criterion for consistency of sets of formulas

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Let be a first order language, and $\Delta\subseteq L$ be a set of sentences. Then $\Delta$ is consistent if and only if every finite subset of $\Delta$ is consistent.

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Cross-references: subset, finite, consistent, sentences, first order language
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This is version 2 of criterion for consistency of sets of formulas, born on 2002-06-04, modified 2002-06-04.
Object id is 3035, canonical name is CriterionForConsistencyOfSetsOfFormulas.
Accessed 3169 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)

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