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  1. Three-elemnt non-finitely axiomatizable matrices and term-equivalence.Katarzyna Pałasińska - 2014 - Logic and Logical Philosophy 23 (4):481-497.
    It was shown in [5] that all two-element matrices are finitely based independently of their classification by term equivalence. In particular, each 2-valued matrix is finitely axiomatizable. We show below that for certain two not finitely axiomatizable 3-valued matrices this property is also preserved under term equivalence. The general problem, whether finite axiomatizability of a finite matrix is preserved under term-equivalence, is still open, as well as the related problem as to whether the consequence operation of a finite matrix is (...)
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  • 2-element matrices.Wolfgang Rautenberg - 1981 - Studia Logica 40 (4):315 - 353.
    Sections 1, 2 and 3 contain the main result, the strong finite axiomatizability of all 2-valued matrices. Since non-strongly finitely axiomatizable 3-element matrices are easily constructed the result reveals once again the gap between 2-valued and multiple-valued logic. Sec. 2 deals with the basic cases which include the important F i from Post's classification. The procedure in Sec. 3 reduces the general problem to these cases. Sec. 4 is a study of basic algebraic properties of 2-element algebras. In particular, we (...)
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  • Matrices, primitive satisfaction and finitely based logics.Janusz Czelakowski - 1983 - Studia Logica 42 (1):89 - 104.
    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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