Studia Logica 44 (1):11 - 24 (1985)

The main result of this paper is the following theorem: a closure space X has an , , Q-regular base of the power iff X is Q-embeddable in It is a generalization of the following theorems:(i) Stone representation theorem for distributive lattices ( = 0, = , Q = ), (ii) universality of the Alexandroff's cube for T 0-topological spaces ( = , = , Q = 0), (iii) universality of the closure space of filters in the lattice of all subsets for , -closure spaces (Q = 0). By this theorem we obtain some characterizations of the closure space given by the consequence operator for the classical propositional calculus over a formalized language of the zero order with the set of propositional variables of the power . In particular we prove that a countable closure space X is embeddable with finite disjunctions preserved into F iff X is a consistent closure space satisfying the compactness theorem and X contains a 0, -base consisting of -prime sets.
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DOI 10.1007/BF00370807
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References found in this work BETA

A Conjunction in Closure Spaces.Andrzej W. Jankowski - 1984 - Studia Logica 43 (4):341 - 351.
Notes on the Rasiowa-Sikorski Lemma.Cecylia Rauszer & Bogdan Sabalski - 1975 - Bulletin of the Section of Logic 4 (3):109-114.

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