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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.
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"compactness" is owned by Aatu.
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| Also defines: |
compactness |
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Cross-references: class, finite, first order logic, consistent, subsets, cardinality, sentences, logic
There are 26 references to this entry.
This is version 2 of compactness, born on 2003-08-06, modified 2003-08-06.
Object id is 4557, canonical name is Compactness.
Accessed 6700 times total.
Classification:
| AMS MSC: | 03B99 (Mathematical logic and foundations :: General logic :: Miscellaneous) |
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Pending Errata and Addenda
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