Characterizing equivalential and algebraizable logics by the Leibniz operator
type: Item
instance of: scholarly article
title: Characterizing equivalential and algebraizable logics by the Leibniz operator
zbMATH Open document ID: 0879.03023
DOI: 10.1023/A:1004979825733
author: Burghard Herrmann
published in: Studia Logica
publication date: 1997-12-22T00:00:00Z
review text: In this paper the author characterizes the hierarchy of protoalgebraic, equivalential, finitely equivalential, possibly infinitely algebraizable and finitely algebraizable logics by properties of the Leibniz operator. The author gives a new short proof of the main result of \textit{W. J. Blok} and \textit{D. Pigozzi} [Algebraizable logics, Mem. Am. Math. Soc. 396 (1989; Zbl 0664.03042)] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics.
Mathematics Subject Classification ID: 03G99
Mathematics Subject Classification ID: 03B22
zbMATH DE Number: 1019355
zbMATH Keywords: algebraizable logic
zbMATH Keywords: Leibniz operator
zbMATH Keywords: protoalgebraic logic
zbMATH Keywords: Beth-definability
reviewed by: Leo Esakia
MaRDI profile type: Publication
full work available at URL: a:1004979825733
OpenAlex ID: W1518264298
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description: scientific article; zbMATH DE number 1019355