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  1. Jarosław Achinger & Andrzej W. Jankowski (1986). On Decidable Consequence Operators. Studia Logica 45 (4):415 - 424.
    The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
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  2. Andrzej W. Jankowski (1986). Retracts of the Closure Space of Filters in the Lattice of All Subsets. Studia Logica 45 (2):135 - 154.
    We give an idea of uniform approach to the problem of characterization of absolute extensors for categories of topological spaces [21], closure spaces [15], Boolean algebras [22], and distributive lattices [4]. In this characterization we use the notion of retract of the closure space of filters in the lattice of all subsets.
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  3. Andrzej W. Jankowski (1986). Some Modifications of Scott's Theorem on Injective Spaces. Studia Logica 45 (2):155 - 166.
    D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.
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  4. Andrzej W. Jankowski (1985). Disjunctions in Closure Spaces. Studia Logica 44 (1):11 - 24.
    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 (...)
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  5. Andrzej W. Jankowski (1985). Galois Structures. Studia Logica 44 (2):109 - 124.
    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 -disjunctive closure space X the dual closure space is topological iff the base of X generated by this dual space consists of the -prime sets in X (Theorem 2). Moreover the characterizations of the satisfiability relation for classical (...)
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  6. Andrzej W. Jankowski (1985). Universality of the Closure Space of Filters in the Algebra of All Subsets. Studia Logica 44 (1):1 - 9.
    In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T 0-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T 0-closure spaces. By this theorem we obtain the following characterization of the consequence (...)
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  7. Andrzej W. Jankowski & Marek Zawadowski (1985). Sheaves Over Heyting Lattices. Studia Logica 44 (3):237 - 256.
    For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.
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  8. Andrzej W. Jankowski (1984). A Conjunction in Closure Spaces. Studia Logica 43 (4):341 - 351.
    This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of -conjunctive closure spaces (X is -conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:1. For every closed and proper subset of an -conjunctive closure space its interior is empty (i.e. it is a boundary (...)
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