Notre Dame Journal of Formal Logic

On Elementary Equivalence for Equality-free Logic

E. Casanovas, P. Dellunde, and R. Jansana


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.

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Notre Dame J. Formal Logic Volume 37, Number 3 (1996), 506-522.

First available in Project Euclid: 14 December 2002

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Zentralblatt MATH identifier

Primary: 03C07: Basic properties of first-order languages and structures
Secondary: 03B10: Classical first-order logic 03C20: Ultraproducts and related constructions


Casanovas, E.; Dellunde, P.; Jansana, R. On Elementary Equivalence for Equality-free Logic. Notre Dame J. Formal Logic 37 (1996), no. 3, 506--522. doi:10.1305/ndjfl/1039886524.

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