14 found
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  1.  7
    A Globalisation of the Gelfand Duality Theorem.Bernhard Banaschewski & Christopher J. Mulvey - 2006 - Annals of Pure and Applied Logic 137 (1):62-103.
    In this paper we bring together results from a series of previous papers to prove the constructive version of the Gelfand duality theorem in any Grothendieck topos , obtaining a dual equivalence between the category of commutative C*-algebras and the category of compact, completely regular locales in the topos.
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  2.  24
    Hüllensysteme und Erweiterung von Quasi-Ordnungen.Bernhard Banaschewski - 1956 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 2 (8-9):117-130.
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  3.  17
    Excluded Middle Versus Choice in a Topos.Bernhard Banaschewski - 2005 - Mathematical Logic Quarterly 51 (3):282.
    It is shown for an arbitrary topos that the Law of the Excluded Middle holds in its propositional logic iff it satisfies the limited choice principle that every epimorphism from 2 = 1 ⊕ 1 splits.
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  4.  14
    Hüllensysteme und Erweiterung von Quasi‐Ordnungen.Bernhard Banaschewski - 1956 - Mathematical Logic Quarterly 2 (8‐9):117-130.
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  5.  32
    The Dual Cantor-Bernstein Theorem and the Partition Principle.Bernhard Banaschewski & Gregory H. Moore - 1990 - Notre Dame Journal of Formal Logic 31 (3):375-381.
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  6.  25
    Algebraic Closure Without Choice.Bernhard Banaschewski - 1992 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 38 (1):383-385.
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  7.  22
    On Principles of Inductive Definition.Bernhard Banaschewski - 1960 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 6 (15-22):248-257.
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  8.  22
    On Some Theorems Equivalent with the Axiom of Choice.Bernhard Banaschewski - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (17-18):279-282.
  9.  26
    A New Proof That “Krull Implies Zorn”.Bernhard Banaschewski - 1994 - Mathematical Logic Quarterly 40 (4):478-480.
    In the present note we give a direct deduction of the Axiom of Choice from the Maximal Ideal Theorem for commutative rings with unit.
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  10.  21
    On Principles of Inductive Definition.Bernhard Banaschewski - 1960 - Mathematical Logic Quarterly 6 (15‐22):248-257.
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  11.  19
    Algebraic Closure Without Choice.Bernhard Banaschewski - 1992 - Mathematical Logic Quarterly 38 (1):383-385.
    This note shows that for the proof of the existence and uniqueness of the algebraic closure of a field one needs only the Boolean Ultrafilter Theorem.
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  12.  12
    Choice Principles and Compactness Conditions.Bernhard Banaschewski - 1998 - Mathematical Logic Quarterly 44 (3):427-430.
    It is shown in Zermelo-Fraenkel Set Theory that Cκ, the Axiom of Choice for κ-indexed families of arbitrary sets, is equivalent to the condition that the frame envelope of any κ-frame is κ-Lindelöf, for any cardinal κ.
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  13.  12
    On Some Theorems Equivalent with the Axiom of Choice.Bernhard Banaschewski - 1961 - Mathematical Logic Quarterly 7 (17‐18):279-282.
  14.  9
    Preface.Bernhard Banaschewski, Thierry Coquand & Giovanni Sambin - 2006 - Annals of Pure and Applied Logic 137 (1-3):1-2.