22 found
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  1.  9
    Recursion Theory and Algebra.G. Metakides, A. Nerode, J. N. Crossley, Iraj Kalantari & Allen Retzlaff - 1986 - Journal of Symbolic Logic 51 (1):229-232.
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  2.  10
    A Blend of Methods of Recursion Theory and Topology.Iraj Kalantari & Larry Welch - 2003 - Annals of Pure and Applied Logic 124 (1-3):141-178.
    This paper is a culmination of our new foundations for recursive analysis through recursive topology as reported in Kalantari and Welch 125; 98 87). While in those papers we developed groundwork for an approach to point free analysis and applied recursion theory, in this paper we blend techniques of recursion theory with those of topology to establish new findings. We present several new techniques different from existing ones which yield interesting results. Incidental to our work is a unifying explanation of (...)
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  3.  14
    Maximal Vector Spaces Under Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari & Allen Retzlaff - 1977 - Journal of Symbolic Logic 42 (4):481-491.
  4.  9
    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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  5.  13
    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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  6.  51
    Simplicity in Effective Topology.Iraj Kalantari & Anne Leggett - 1982 - Journal of Symbolic Logic 47 (1):169-183.
  7.  58
    Effective Extensions of Linear Forms on a Recursive Vector Space Over a Recursive Field.R. G. Downey & Iraj Kalantari - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (13):193-200.
  8.  16
    Degrees of Recursively Enumerable Topological Spaces.Iraj Kalantari & J. B. Remmel - 1983 - Journal of Symbolic Logic 48 (3):610-622.
  9.  11
    Recursive Constructions in Topological Spaces.Iraj Kalantari & Allen Retzlaff - 1979 - Journal of Symbolic Logic 44 (4):609-625.
    We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space X. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in X.
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  10.  18
    Maximality in Effective Topology.Iraj Kalantari & Anne Leggett - 1983 - Journal of Symbolic Logic 48 (1):100-112.
  11.  13
    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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  12.  6
    Effective Topological Spaces III: Forcing and Definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36 (1):17-27.
  13.  21
    Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):385-401.
  14.  29
    Major Subspaces of Recursively Enumerable Vector Spaces.Iraj Kalantari - 1978 - Journal of Symbolic Logic 43 (2):293-303.
  15.  10
    Effective Topological Spaces I: A Definability Theory.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (1):1-27.
  16.  14
    Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari - 1979 - Mathematical Logic Quarterly 25 (25‐29):385-401.
  17.  8
    A Blend of Methods of Recursion Theory and Topology: A Π1 0 Tree of Shadow Points. [REVIEW]Iraj Kalantari & Larry Welch - 2004 - Archive for Mathematical Logic 43 (8):991-1008.
    This paper is a sequel to our [7]. In that paper we constructed a Π1 0 tree of avoidable points. Here we construct a Π1 0 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2<ω. One interesting fact is that while our Π1 0 tree (...)
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  18.  18
    Density and Baire Category in Recursive Topology.Iraj Kalantari & Larry Welch - 2004 - Mathematical Logic Quarterly 50 (45):381-391.
    We develop the concepts of recursively nowhere dense sets and sets that are recursively of first category and study closed sets of points in light of Baire's Category Theorem. Our theorems are primarily concerned with exdomains of recursive quantum functions and hence with avoidable points . An avoidance function is a recursive function which can be used to expel avoidable points from domains of recursive quantum functions. We define an avoidable set of points to be an arbitrary subset of the (...)
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  19.  16
    Preface.Ali Enayat & Iraj Kalantari - 2010 - Annals of Pure and Applied Logic 161 (6):709-710.
  20.  18
    On Turing Degrees of Points in Computable Topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.
    This paper continues our study of computable point-free topological spaces and the metamathematical points in them. For us, a point is the intersection of a sequence of basic open sets with compact and nested closures. We call such a sequence a sharp filter. A function fF from points to points is generated by a function F from basic open sets to basic open sets such that sharp filters map to sharp filters. We restrict our study to functions that have at (...)
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  21.  13
    On Degree-Preserving Homeomorphisms Between Trees in Computable Topology.Iraj Kalantari & Larry Welch - 2008 - Archive for Mathematical Logic 46 (7-8):679-693.
    In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong ${\Pi^0_2}$ class and a bounded ${\Pi^0_1}$ class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented ${\mathbb{R}^n}$ , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence (...)
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  22.  10
    When Series of Computable Functions with Varying Domains Are Computable.Iraj Kalantari & Larry Welch - 2013 - Mathematical Logic Quarterly 59 (6):471-493.