7 found
  1.  4
    On the Uniform Computational Content of the Baire Category Theorem.Vasco Brattka, Matthew Hendtlass & Alexander P. Kreuzer - 2018 - Notre Dame Journal of Formal Logic 59 (4):605-636.
    We study the uniform computational content of different versions of the Baire category theorem in the Weihrauch lattice. The Baire category theorem can be seen as a pigeonhole principle that states that a complete metric space cannot be decomposed into countably many nowhere dense pieces. The Baire category theorem is an illuminating example of a theorem that can be used to demonstrate that one classical theorem can have several different computational interpretations. For one, we distinguish two different logical versions of (...)
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  2.  23
    The Intermediate Value Theorem in Constructive Mathematics Without Choice.Matthew Hendtlass - 2012 - Annals of Pure and Applied Logic 163 (8):1050-1056.
  3.  13
    Continuous Isomorphisms From R Onto a Complete Abelian Group.Douglas Bridges & Matthew Hendtlass - 2010 - Journal of Symbolic Logic 75 (3):930-944.
    This paper provides a Bishop-style constructive analysis of the contrapositive of the statement that a continuous homomorphism of R onto a compact abelian group is periodic. It is shown that, subject to a weak locatedness hypothesis, if G is a complete (metric) abelian group that is the range of a continuous isomorphism from R, then G is noncompact. A special case occurs when G satisfies a certain local path-connectedness condition at 0. A number of results about one-one and injective mappings (...)
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  4.  8
    Continuous Homomorphisms of R Onto a Compact Group.Douglas Bridges & Matthew Hendtlass - 2010 - Mathematical Logic Quarterly 56 (2):191-197.
    It is shown within Bishop's constructive mathematics that, under one extra, classically automatic, hypothesis, a continuous homomorphism from R onto a compact metric abelian group is periodic, but that the existence of the minimum value of the period is not derivable.
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    Bishop's Lemma.Hannes Diener & Matthew Hendtlass - 2018 - Mathematical Logic Quarterly 64 (1-2):49-54.
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  6.  15
    Reverse Mathematics, Well-Quasi-Orders, and Noetherian Spaces.Emanuele Frittaion, Matthew Hendtlass, Alberto Marcone, Paul Shafer & Jeroen Van der Meeren - 2016 - Archive for Mathematical Logic 55 (3-4):431-459.
    A quasi-order Q induces two natural quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}}$$\end{document}, but if Q is a well-quasi-order, then these quasi-orders need not necessarily be well-quasi-orders. Nevertheless, Goubault-Larrecq, pp. 453–462, 2007) showed that moving from a well-quasi-order Q to the quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{P}}$$\end{document} preserves well-quasi-orderedness in a topological sense. Specifically, Goubault-Larrecq proved that the upper topologies of the induced quasi-orders on P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} (...)
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  7.  5
    A Direct Proof of Wiener's Theorem.Matthew Hendtlass & Peter Schuster - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 293--302.
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