Characterizing classes defined with equality
First order languages without equality are considered in the paper under review. The author introduces a weak form of equality predicate, the Leibniz equality. The author defines two distinct complete semantics (full and reduced). Reduced semantics is defined using the Leibniz equality. Characterizations of both the full and the reduced model classes of certain theories (elementary, universal, universal Horn, and universal atomic theories) are given in the form of Birkhoff-type theorems. Examples making clear the difference between the two semantics for the theories are given.
scientific article; zbMATH DE number 1071487