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On elementary equivalence for equality-free logic. (English) Zbl 0869.03007

Summary: 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-Fraïssé type theorem. We also give characterizations of elementary classes in equality-free logic. As a by-product we characterize the sentences that are logically equivalent to an equality-free one.

MSC:

03B20 Subsystems of classical logic (including intuitionistic logic)
03C07 Basic properties of first-order languages and structures
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