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 that is countably compact and has Löwenheim number ω.[2]
See also edit
- Abstract algebraic logic – Study of the algebraization of deductive systems, based on the Lindenbaum–Tarski algebra
- Abstract model theory
- Löwenheim number – smallest cardinal number for which a weak downward Löwenheim–Skolem theorem holds
- Lindström's theorem
- Universal logic – Subfield of logic that studies the features common to all logical systems
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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