Free equivalential algebras
type: Item
instance of: scholarly article
title: Free equivalential algebras
zbMATH Open document ID: 1154.08002
author: Katarzyna Słomczyńska
published in: Annals of Pure and Applied Logic
publication date: 2008-11-12T00:00:00Z
review text: An equivalential algebra is a groupoid \(A=(A,\leftrightarrow )\) that is a subreduct of a Brouwerian semilattice (or, equivalently, a Heyting algebra) with the operation \(\leftrightarrow \) given by \( x\leftrightarrow y=(x\rightarrow y)\wedge (y\rightarrow x).\) This notation was introduced by \textit{J. K. Kabziński} and \textit{A. Wroński} [``On equivalential algebras'', in: Proc. 1975 International Symposium on Multiple-Valued Logic, Indiana Univ., Bloomington, Ind., 1975. Long Beach, Calif.: IEEE Comput. Soc., 419--428 (1975)] as an algebraic counterpart of the equivalential fragment of intuitionistic propositional logic. The class \( \mathcal{E}\) of all equivalential algebras is equationally definable by the following identities: \(xxy=y,xyzz=xz(yz),xy(xzz)(xzz)=xy\). In this paper the author shows how to construct effectively the free finitely generated algebras in \(\mathcal{E}.\)
Mathematics Subject Classification ID: 08B20
Mathematics Subject Classification ID: 03B20
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 5365118
zbMATH Keywords: intuitionistic logic
zbMATH Keywords: equivalence
zbMATH Keywords: free algebras
zbMATH Keywords: equivalential algebras
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: j.apal.2008.03.003
OpenAlex ID: W2064608708
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DOI: 10.1016/J.APAL.2008.03.003
description: scientific article; zbMATH DE number 5365118