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

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
Categories