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# compactness

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.

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compactness

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## Mathematics Subject Classification

03B99*no label found*

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