Abstract logic

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

• Abstract algebraic logic
• Abstract model theory
• Löwenheim number
• Lindström's theorem
• Universal logic

References