Abstract logic

For the musical album please see Abstract Logic (album)

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 which is countably compact and has Löwenheim number ω.

See also

• Löwenheim number
• Lindström's theorem