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  1. The lattice of strengthenings of a strongly finite consequence operation.Wiesław Dziobiak - 1981 - Studia Logica 40 (2):177 - 193.
    First, we prove that the lattice of all structural strengthenings of a given strongly finite consequence operation is both atomic and coatomic, it has finitely many atoms and coatoms, each coatom is strongly finite but atoms are not of this kind — we settle this by constructing a suitable counterexample. Second, we deal with the notions of hereditary: algebraicness, strong finitisticity and finite approximability of a strongly finite consequence operation. Third, we formulate some conditions which tell us when the lattice (...)
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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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  • 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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  • An example concerning the lattice of the structural consequence operations.Wies law Dziobiak - 1979 - Bulletin of the Section of Logic 8 (2):48-52.
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