# Abstract logic

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In mathematical logic, an **abstract logic** is a formal system consisting of a class of sentences and a satisfaction relation with specific properties related to occurrence, expansion, isomorphism, renaming and quantification.^{[1]}

Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic which is countably compact and has Löwenheim number ω.^{[2]}

## See also[edit]

## References[edit]

**^**C. C. Chang and Jerome Keisler*Model Theory*, 1990 ISBN 0-444-88054-2 page 128**^**C. C. Chang and Jerome Keisler*Model Theory*, 1990 ISBN 0-444-88054-2 page 132

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