13 found
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  1.  15
    Sequences of Real Functions on [0, 1] in Constructive Reverse Mathematics.Hannes Diener & Iris Loeb - 2009 - Annals of Pure and Applied Logic 157 (1):50-61.
    We give an overview of the role of equicontinuity of sequences of real-valued functions on [0,1] and related notions in classical mathematics, intuitionistic mathematics, Bishop’s constructive mathematics, and Russian recursive mathematics. We then study the logical strength of theorems concerning these notions within the programme of Constructive Reverse Mathematics. It appears that many of these theorems, like a version of Ascoli’s Lemma, are equivalent to fan-theoretic principles.
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  2.  10
    The Pseudocompactness of [0.1] Is Equivalent to the Uniform Continuity Theorem.Douglas Bridges & Hannes Diener - 2007 - Journal of Symbolic Logic 72 (4):1379 - 1384.
    We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space into a metric space, it is necessary and sufficient to prove any of a number of equivalent conditions, such as that every pointwise continuous mapping of [0, 1] into R is bounded. The proofs are analytic, making no use of, for example, fan-theoretic ideas.
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  3.  15
    The Anti-Specker Property, Positivity, and Total Boundedness.Douglas Bridges & Hannes Diener - 2010 - Mathematical Logic Quarterly 56 (4):434-441.
    Working within Bishop-style constructive mathematics, we examine some of the consequences of the anti-Specker property, known to be equivalent to a version of Brouwer's fan theorem. The work is a contribution to constructive reverse mathematics.
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  4.  10
    A Constructive Treatment of Urysohn's Lemma in an Apartness Space.Douglas Bridges & Hannes Diener - 2006 - Mathematical Logic Quarterly 52 (5):464-469.
    This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant constructive version (...)
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  5.  2
    Generalising Compactness.Hannes Diener - 2008 - Mathematical Logic Quarterly 54 (1):49-57.
    Working within the framework of Bishop's constructive mathematics, we will show that it is possible to define compactness in a more general setting than that of uniform spaces. It is also shown that it is not possible to do this in a topological space.
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  6.  6
    Bishop's Lemma.Hannes Diener & Matthew Hendtlass - 2018 - Mathematical Logic Quarterly 64 (1-2):49-54.
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  7.  9
    Reclassifying the Antithesis of Specker’s Theorem.Hannes Diener - 2012 - Archive for Mathematical Logic 51 (7-8):687-693.
    It is shown that a principle, which can be seen as a constructivised version of sequential compactness, is equivalent to a form of Brouwer’s fan theorem. The complexity of the latter depends on the geometry of the spaces involved in the former.
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  8.  3
    Contents.Dieter Spreen, Hannes Diener & Vasco Brattka - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter.
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  9.  3
    Index.Dieter Spreen, Hannes Diener & Vasco Brattka - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 411-414.
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  10.  3
    Preface.Dieter Spreen, Hannes Diener & Vasco Brattka - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter.
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  11.  3
    Principles Weaker Than BD-N.Robert S. Lubarsky & Hannes Diener - 2013 - Journal of Symbolic Logic 78 (3):873-885.
  12.  2
    Separating the Fan Theorem and its Weakenings.Robert S. Lubarsky & Hannes Diener - 2014 - Journal of Symbolic Logic 79 (3):792-813.
    Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be strict, others strict in a weak context, and yet others not at all, using disparate techniques. Here we present a family of related Kripke models which separates all of the as yet identified fan theorems.
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  13.  5
    Logic, Computation, Hierarchies.Dieter Spreen, Hannes Diener & Vasco Brattka - unknown
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