Abstract logic

For other uses of "Abstract logic", see Abstract logic (disambiguation).

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

References

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