## Notre Dame Journal of Formal Logic

### On Elementary Equivalence for Equality-free Logic

#### 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.

#### Article information

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

Dates
First available: 14 December 2002

http://projecteuclid.org/euclid.ndjfl/1039886524

Mathematical Reviews number (MathSciNet)
MR1434433

Digital Object Identifier
doi:10.1305/ndjfl/1039886524

Zentralblatt MATH identifier
0869.03007

#### Citation

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

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