Characterizing classes defined without Equality

@inproceedings{Elgueta1997CharacterizingCD,
  title={Characterizing classes defined without Equality},
  author={R. Elgueta},
  year={1997}
}
In this paper we mainly deal with first-order languages without equality and introduce a weak form of equality predicate, the so-called Leibniz equality. This equality is characterized algebraically by means of a natural concept of congruence; in any structure, it turns out to be the maximum congruence of the structure. We show that first-order logic without equality has two distinct complete semantics (full semantics and reduced semantics) related by a reduction operator. The last and main… CONTINUE READING

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