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. Based on Lindström's characterization, first-order logic is, up to equivalence, the only abstract logic that is countably compact and has Löwenheim number ω.
See also Abstract algebraic logic – Aspect of mathematical logic Abstract model theory Löwenheim number – Smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds Lindström's theorem – Theorem in mathematical logic Universal logic – Subfield of logic that studies the features common to all logical systems
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