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  1. Some theorems on structural entailment relations.Janusz Czelakowski - 1983 - Studia Logica 42 (4):417 - 429.
    The classesMatr( ) of all matrices (models) for structural finitistic entailments are investigated. The purpose of the paper is to prove three theorems: Theorem I.7, being the counterpart of the main theorem from Czelakowski [3], and Theorems II.2 and III.2 being the entailment counterparts of Bloom's results [1]. Theorem I.7 states that if a classK of matrices is adequate for , thenMatr( ) is the least class of matrices containingK and closed under the formation of ultraproducts, submatrices, strict homomorphisms and (...)
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  • Reduced products of logical matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.
    The class Matr(C) of all matrices for a prepositional logic (, C) is investigated. The paper contains general results with no special reference to particular logics. The main theorem (Th. (5.1)) which gives the algebraic characterization of the class Matr(C) states the following. Assume C to be the consequence operation on a prepositional language induced by a class K of matrices. Let m be a regular cardinal not less than the cardinality of C. Then Matr (C) is the least class (...)
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  • Another proof that ISP r is the least quasivariety containing K.Janusz Czelakowski & Wies?aw Dziobiak - 1982 - Studia Logica 41 (4):343 - 345.
    Let q(K) denote the least quasivariety containing a given class K of algebraic structures. Mal'cev [3] has proved that q(K) = ISP r(K)(1). Another description of q(K) is given in Grätzer and Lakser [2], that is, q(K) = ISPP u(K)2. We give here other proofs of these results. The method which enables us to do that is borrowed from prepositional logics (cf. [1]).
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  • Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.
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  • Definability of Leibniz equality.R. Elgueta & R. Jansana - 1999 - Studia Logica 63 (2):223-243.
    Given a structure for a first-order language L, two objects of its domain can be indiscernible relative to the properties expressible in L, without using the equality symbol, and without actually being the same. It is this relation that interests us in this paper. It is called Leibniz equality. In the paper we study systematically the problem of its definibility mainly for classes of structures that are the models of some equality-free universal Horn class in an infinitary language Lκκ, where (...)
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  • Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
    W. J. Blok and Don Pigozzi set out to try to answer the question of what it means for a logic to have algebraic semantics. In this seminal book they transformed the study of algebraic logic by giving a general framework for the study of logics by algebraic means. The Dutch mathematician W. J. Blok (1947-2003) received his doctorate from the University of Amsterdam in 1979 and was Professor of Mathematics at the University of Illinois, Chicago until his death in (...)
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  • Model Theory.C. C. Chang & H. Jerome Keisler - 1992 - Studia Logica 51 (1):154-155.
     
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