### On Elementary Equivalence for Equality-free Logic

E. Casanovas, P. Dellunde, and R. Jansana
Source: Notre Dame J. Formal Logic Volume 37, Number 3 (1996), 506-522.

#### Abstract

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.

First Page:
Primary Subjects: 03C07
Secondary Subjects: 03B10, 03C20
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1039886524
Mathematical Reviews number (MathSciNet): MR1434433
Digital Object Identifier: doi:10.1305/ndjfl/1039886524
Zentralblatt MATH identifier: 0869.03007

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