9 found
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  1.  19
    Effective topological spaces I: A definability theory.Iraj Kalantari & Galen Weitkamp - 1985 - Annals of Pure and Applied Logic 29 (1):1-27.
  2.  26
    Effective topological spaces II: A hierarchy.Iraj Kalantari & Galen Weitkamp - 1985 - 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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  3.  14
    Effective topological spaces III: Forcing and definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36:17-27.
  4.  16
    Analytic sets having incomparable Kleene degrees.Galen Weitkamp - 1982 - Journal of Symbolic Logic 47 (4):860-868.
  5.  38
    High and low Kleene degrees of coanalytic sets.Stephen G. Simpson & Galen Weitkamp - 1983 - Journal of Symbolic Logic 48 (2):356-368.
  6.  5
    Iterating the Superjump Along Definable Prewellorderings.Galen Weitkamp - 1982 - Mathematical Logic Quarterly 28 (27‐32):385-394.
  7.  20
    Iterating the Superjump Along Definable Prewellorderings.Galen Weitkamp - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (27-32):385-394.
  8.  20
    On the Existence and Recursion Theoretic Properties of ∑n1-Generic Sets of Reals.Galen Weitkamp - 1985 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 31 (7-8):97-108.
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  9.  29
    The Σ 2 1 theory of axioms of symmetry.Galen Weitkamp - 1989 - Journal of Symbolic Logic 54 (3):727-734.
    The axiom of symmetry (A ℵ 0 ) asserts that for every function F: ω 2 → ω 2 there is a pair of reals x and y in ω 2 so that y is not in the countable set $\{(F(x))_n:n coded by F(x) and x is not in the set coded by F(y). A(Γ) denotes axiom A ℵ 0 with the restriction that graph(F) belongs to the pointclass Γ. In § 2 we prove A(Σ 1 1 ). In § (...)
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