8 found
Order:
  1.  27
    Universality of the Closure Space of Filters in the Algebra of All Subsets.Andrzej W. Jankowski - 1985 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  2.  40
    A Conjunction in Closure Spaces.Andrzej W. Jankowski - 1984 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  3.  36
    Some Modifications of Scott's Theorem on Injective Spaces.Andrzej W. Jankowski - 1986 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  4.  15
    Retracts of the Closure Space of Filters in the Lattice of All Subsets.Andrzej W. Jankowski - 1986 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  56
    On Decidable Consequence Operators.Jaros?aw Achinger & Andrzej W. Jankowski - 1986 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  6.  39
    Disjunctions in Closure Spaces.Andrzej W. Jankowski - 1985 - 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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  7.  35
    Galois Structures.Andrzej W. Jankowski - 1985 - 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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  8.  18
    Sheaves Over Heyting Lattices.Andrzej W. Jankowski & Marek Zawadowski - 1985 - 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.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark