Abstract
We examine the notion of primitive satisfaction in logical matrices. Theorem II. 1, being the matrix counterpart of Baker's well-known result for congruently distributive varieties of algebras (cf [1], Thm. 1.5), links the notions of primitive and standard satisfaction. As a corollary we give the matrix version of Jónsson's Lemma, proved earlier in [4]. Then we investigate propositional logics with disjunction. The main result, Theorem III. 2, states a necessary and sufficient condition for such logics to be finitely based.
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Czelakowski, J. Matrices, primitive satisfaction and finitely based logics. Stud Logica 42, 89–104 (1983). https://doi.org/10.1007/BF01418762
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DOI: https://doi.org/10.1007/BF01418762