Name
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 provid- ing some Keisler-Shelah type ultrapower theorems and an Ehrenfeucht-Fra¨ isse 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. 1I ntroduction In first-order logic it is common to employ one symbol for the equality relation. Equality is considered a logical notion, with a fixed meaning. This was not the case when the first investigations in mathematical logic took place, but this practice has been strongly supported by successful applications to mathematical theories. Thus, the general study of first-order logic without equality, or equality-free logic ,a sw eprefer to call it, has been neglected in favor of the more powerful version with equality. Recently some interest in fragments of equality-free logic has arisen in the frame of algebraic logic (see Blok and Pigozzi (5) and Bloom (2)). We think that a model-theoretic study of equality-free logic is worthwhile by itself and we hope that, by means of contrast with the well-known results for first-order logic, this study will contribute to the understanding of the role of equality in mathematical theories and structures. As an easy example of this comparison consider the fact that every satisfiable set of equality-free sentences has an infinite model. Let L be a similarity type. The set of equality-free formulas of L, that is, the set of all first-order formulas of L not containing the equality symbol, is denoted by L−. Given two L-structures A, B with A ≡− B we mean that A and B satisfy exactly the same sentences of L− .W edevote this paper to the study of algebraic characteri- zations of the relation ≡− and of elementary classes in the sense of L−. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1305/ndjfl/1039886524 | Notre Dame Journal of Formal Logic |
Keywords | Field | DocType |
algebraic logic,first order,first order logic,satisfiability | Algebraic sentence,Discrete mathematics,Algebra,Algorithm,Substructural logic,Free logic,Predicate functor logic,Many-valued logic,Predicate logic,Intermediate logic,Mathematics,Dynamic logic (modal logic) | Journal |
Volume | Issue | Citations |
37 | 3 | 15 |
PageRank | References | Authors |
1.29 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Enrique Casanovas | 1 | 57 | 11.79 |
| Pilar Dellunde | 2 | 156 | 22.63 |
| Ramon Jansana | 3 | 389 | 47.83 |