Matrices, primitive satisfaction and finitely based logics
type: Item
instance of: scholarly article
title: Matrices, primitive satisfaction and finitely based logics
zbMATH Open document ID: 0599.03030
DOI: 10.1007/BF01418762
author: Janusz Czelakowski
published in: Studia Logica
publication date: 1983-01-01T00:00:00Z
review text: \textit{K. A. Baker}'s primitive satisfaction theorem (stated for congruence-distributive equational classes of algebras [cf. Trans. Am. Math. Soc. 190, 125-150 (1974; Zbl 0291.08001)]) is modified and reformulated so as to apply to a class of logical matrices Matr(C) such that the lattice of C-filters is distributive. A matrix version of Jónsson's lemma is a corollary to this theorem. Then some properties of propositional logics with disjunction are studied. The main result states that a standard finitely equivalent logic C with disjunction can be axiomatized by a finite number of rule schemata if and only if the class of finitely subdirectly irreducible matrices in the class Matr(C) is finitely (first-order) axiomatizable.
Mathematics Subject Classification ID: 03B99
zbMATH DE Number: 3966040
zbMATH Keywords: axiomatizability
zbMATH Keywords: primitive satisfaction theorem
zbMATH Keywords: logical matrices
zbMATH Keywords: lattice of C-filters
zbMATH Keywords: matrix version of Jónsson's lemma
zbMATH Keywords: propositional logics with disjunction
zbMATH Keywords: equivalent logic
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3966040