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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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  • Recursive and Nonextendible Functions Over the Reals; Filter Foundation for Recursive Analysis.II.Iraj Kalantari & Lawrence Welch - 1999 - Annals of Pure and Applied Logic 98 (1-3):87-110.
    In this paper we continue our work of Kalantari and Welch . There we introduced machinery to produce a point-free approach to points and functions on topological spaces and found conditions for both which lend themselves to effectivization. While we studied recursive points in that paper, here, we present two useful classes of recursive functions on topological spaces, apply them to the reals, and find precise accounting for the nature of the properties of some examples that exist in the literature. (...)
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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.
  • 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 III: Forcing and Definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36 (1):17-27.