PlanetMath: compactness

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compactness

(Definition)

A logic is said to be $(\kappa,\lambda)$ -compact, if the following holds

If $\Phi$ is a set of sentences of cardinality less than or equal to $\kappa$ and all subsets of $\Phi$ of cardinality less than $\lambda$ are consistent, then $\Phi$ is consistent.

For example, first order logic is $(\omega,\omega)$ -compact, for if all finite subsets of some class of sentences are consistent, so is the class itself.

"compactness" is owned by Aatu.

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compactness

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Cross-references: class, finite, first order logic, consistent, subsets, cardinality, sentences, logic
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This is version 2 of compactness, born on 2003-08-06, modified 2003-08-06.
Object id is 4557, canonical name is Compactness.
Accessed 5822 times total.

Classification:

AMS MSC:

03B99 (Mathematical logic and foundations :: General logic :: Miscellaneous)

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