On definability of the equality in classes of algebras with an equivalence relation
type: Item
instance of: scholarly article
title: On definability of the equality in classes of algebras with an equivalence relation
zbMATH Open document ID: 0956.03053
DOI: 10.1023/A:1005237627378
author: Pilar Dellunde
published in: Studia Logica
publication date: 2001-03-07T00:00:00Z
review text: In an earlier paper, the author has presented [``A finitary 1-equivalential logic not finitely equivalential'', Bull. Sect. Log., Univ. Lódź, Dep. Log. 24, No. 3, 120-123 (1995; Zbl 0841.03037)] a (finitary) regularly algebraizable logic in the similarity type \(\{\leftrightarrow\}\) that is not finitely equivalential. It is now shown that such logics exist in every similarity type containing \(\leftrightarrow\). As a consequence, the following model-theoretic result concerning algebras with an equivalence relation is obtained: for any algebraic similarity type, there are classes of such algebras in which equality is definable by a set of atomic formulas, but not by a finite set of such formulas.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03C40
zbMATH DE Number: 1501386
zbMATH Keywords: algebraizable logics
zbMATH Keywords: equivalential logics
zbMATH Keywords: Leibniz congruence
zbMATH Keywords: model theory
MaRDI profile type: Publication
full work available at URL: a:1005237627378
OpenAlex ID: W2182510467
description: scientific article; zbMATH DE number 1501386