On Elementary Equivalence for Equality-free Logic

  title={On Elementary Equivalence for Equality-free Logic},
  author={Enrique Casanovas and Pilar Dellunde and Ramon Jansana},
  journal={Notre Dame Journal of Formal Logic},
This paper is a contribution to the study of equality-free logic, that is, first-order logic without equality. We mainly devote ourselves to the study of algebraic characterizations of its relation of elementary equivalence by providing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fra ı̈sśe type theorem. We also give characterizations of elementary classes in equalityfree logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free… CONTINUE READING

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