Abstract
This paper is a continuation of investigations on Galois connections from [1], [3], [10]. It is a continuation of [2]. We have shown many results that link properties of a given closure space with that of the dual space. For example: for every ω-disjunctive closure space X the dual closure space is topological iff the base of X generated by this dual space consists of the ω-prime sets in X (Theorem 2). Moreover the characterizations of the satisfiability relation for classical logic are shown. Roughly speaking our main result here is the following: a satisfiability relation in a logic L with, a countable language is a fragment of the classical one iff the compactness theorem for L holds (Theorems 3–8).
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Jankowski, A.W. Galois structures. Stud Logica 44, 109–124 (1985). https://doi.org/10.1007/BF00379761
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DOI: https://doi.org/10.1007/BF00379761