The lattice of strengthenings of a strongly finite consequence operation

Studia Logica 40 (2):177 - 193 (1981)
Abstract
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 of all structural strengthenings of a given strongly finite consequence operation is finite, and subsequently we give some applications of them.
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DOI 10.1007/BF01874707
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Reduced Products of Logical Matrices.Janusz Czelakowski - 1980 - Studia Logica 39 (1):19 - 43.
A Theorem About Infinite-Valued Sentential Logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.

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Equivalential Logics (II).Janusz Czelakowski - 1981 - Studia Logica 40 (4):355 - 372.

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