Quasivarieties of logic, regularity conditions and parameterized algebraization
type: Item
instance of: scholarly article
title: Quasivarieties of logic, regularity conditions and parameterized algebraization
zbMATH Open document ID: 1039.08005
DOI: 10.1023/A:1024673906579
author: G. D. Barbour
author: J. G. Raftery
published in: Studia Logica
publication date: 2004-02-15T00:00:00Z
review text: The authors exploit the many formal similarities between quasivarieties of logic and relatively congruence-regular quasivarieties. Indeed, they develop a unifying model for them which extends the Blok-Pigozzi theory of algebraizable deductive systems. The development includes the detailed proof of many theorems, the presentation of several useful examples of the results, an important counterexample (a quasivariety need not be \(t\)-deductive for every \(t\)), and an application of the authors' theory to algebraic coherence. Finally, the authors' theory has the bonus of connections to homological algebra and congruence-class geometries. Unsolved problem (2003): Prove or disprove that \(t\)-regular quasivarieties are \(t\)-deductive.
reviewed by: Albert A. Mullin
Mathematics Subject Classification ID: 08C15
Mathematics Subject Classification ID: 03G99
zbMATH DE Number: 2042711
zbMATH Keywords: algebraic logic
zbMATH Keywords: deductive systems
zbMATH Keywords: coherence
zbMATH Keywords: regularity
zbMATH Keywords: quasivarieties
zbMATH Keywords: algebraic coherence
MaRDI profile type: Publication
full work available at URL: a:1024673906579
OpenAlex ID: W1519453649
description: scientific article; zbMATH DE number 2042711