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  1. Effective Inseparability in a Topological Setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.
    Effective inseparability of pairs of sets is an important notion in logic and computer science. We study the effective inseparability of sets which appear as index sets of subsets of an effectively given topological T0-space and discuss its consequences. It is shown that for two disjoint subsets X and Y of the space one can effectively find a witness that the index set of X cannot be separated from the index set of Y by a recursively enumerable set, if X (...)
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  • Point-Free Topological Spaces, Functions and Recursive Points; Filter Foundation for Recursive Analysis. I.Iraj Kalantari & Lawrence Welch - 1998 - Annals of Pure and Applied Logic 93 (1-3):125-151.
    In this paper we develop a point-free approach to the study of topological spaces and functions on them, establish platforms for both and present some findings on recursive points. In the first sections of the paper, we obtain conditions under which our approach leads to the generation of ideal objects with which mathematicians work. Next, we apply the effective version of our approach to the real numbers, and make exact connections to the classical approach to recursive reals. In the succeeding (...)
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  • Effective Topological Spaces II: A Hierarchy.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (2):207-224.
    This paper is an investigation of definability hierarchies on effective topological spaces. An open subset U of an effective space X is definable iff there is a parameter free definition φ of U so that the atomic predicate symbols of φ are recursively open relations on X . The complexity of a definable open set may be identified with the quantifier complexity of its definition. For example, a set U is an ∃∃∀∃-set if it has an ∃∃∀∃ parameter free definition (...)
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  • Effective Topological Spaces I: A Definability Theory.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (1):1-27.
  • The Undecidability of the Lattice of R.E. Closed Subsets of an Effective Topological Space.Sheryl Silibovsky Brady & Jeffrey B. Remmel - 1987 - Annals of Pure and Applied Logic 35 (2):193-203.
    The first-order theory of the lattice of recursively enumerable closed subsets of an effective topological space is proved undecidable using the undecidability of the first-order theory of the lattice of recursively enumerable sets. In particular, the first-order theory of the lattice of recursively enumerable closed subsets of Euclidean n -space, for all n , is undecidable. A more direct proof of the undecidability of the lattice of recursively enumerable closed subsets of Euclidean n -space, n ⩾ 2, is provided using (...)
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  • Effective Topological Spaces III: Forcing and Definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36 (1):17-27.