Results for 'Douglas S. Bridges'

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  1.  39
    Constructive mathematics and unbounded operators — a reply to Hellman.Douglas S. Bridges - 1995 - Journal of Philosophical Logic 24 (5):549 - 561.
    It is argued that Hellman's arguments purporting to demonstrate that constructive mathematics cannot cope with unbounded operators on a Hilbert space are seriously flawed, and that there is no evidence that his thesis is correct.
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  2.  34
    Constructive notions of equicontinuity.Douglas S. Bridges - 2009 - Archive for Mathematical Logic 48 (5):437-448.
    In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.
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  3.  96
    Can constructive mathematics be applied in physics?Douglas S. Bridges - 1999 - Journal of Philosophical Logic 28 (5):439-453.
    The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.
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  4.  24
    Product a-frames and proximity.Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (1):12-26.
    Continuing the study of apartness in lattices, begun in [8], this paper deals with axioms for a product a-frame and with their consequences. This leads to a reasonable notion of proximity in an a-frame, abstracted from its counterpart in the theory of set-set apartness.
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  5.  35
    Reflections on function spaces.Douglas S. Bridges - 2012 - Annals of Pure and Applied Logic 163 (2):101-110.
  6. Uniformly convex Banach spaces are reflexive—constructively.Douglas S. Bridges, Hajime Ishihara & Maarten McKubre-Jordens - 2013 - Mathematical Logic Quarterly 59 (4-5):352-356.
    We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the Milman-Pettis theorem that uniformly convex Banach spaces are reflexive.
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  7.  13
    On Weak Operator Compactness of the Unit Ball of L(H).Douglas S. Bridges - 1978 - Mathematical Logic Quarterly 24 (31‐36):493-494.
  8.  25
    On Weak Operator Compactness of the Unit Ball of L_( _H).Douglas S. Bridges - 1978 - Mathematical Logic Quarterly 24 (31-36):493-494.
  9.  24
    Glueing continuous functions constructively.Douglas S. Bridges & Iris Loeb - 2010 - Archive for Mathematical Logic 49 (5):603-616.
    The glueing of (sequentially, pointwise, or uniformly) continuous functions that coincide on the intersection of their closed domains is examined in the light of Bishop-style constructive analysis. This requires us to pay attention to the way that the two domains intersect.
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  10.  21
    Church's Thesis and Bishop's Constructivism.Douglas S. Bridges - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--58.
  11.  2
    Church’s Thesis and Bishop’s Constructivism.Douglas S. Bridges - 2006 - In Adam Olszewski, Jan Wolenski & Robert Janusz (eds.), Church's Thesis After 70 Years. Ontos Verlag. pp. 58-65.
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  12.  13
    Complements of Intersections in Constructive Mathematics.Douglas S. Bridges & Hajime Ishihara - 1994 - Mathematical Logic Quarterly 40 (1):35-43.
    We examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and (...)
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  13.  21
    A Note on Morse's Lambda‐Notation in Set Theory.Douglas S. Bridges - 1978 - Mathematical Logic Quarterly 24 (8):113-114.
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  14.  34
    A Note on Morse's Lambda-Notation in Set Theory.Douglas S. Bridges - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (8):113-114.
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  15.  33
    Compactness notions for an apartness space.Douglas S. Bridges - 2012 - Archive for Mathematical Logic 51 (5-6):517-534.
    Two new notions of compactness, each classically equivalent to the standard classical one of sequential compactness, for apartness spaces are examined within Bishop-style constructive mathematics.
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  16.  17
    How to construct a product of a‐frames.Douglas S. Bridges - 2012 - Mathematical Logic Quarterly 58 (4-5):281-293.
    It is shown how, under certain circumstances and within Bishop‐style constructive mathematics, one can construct a product of two a‐frames (the structures underlying the constructive theory of apartness on frames).
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  17.  20
    Constructive complements of unions of two closed sets.Douglas S. Bridges - 2004 - Mathematical Logic Quarterly 50 (3):293.
    It is well known that in Bishop-style constructive mathematics, the closure of the union of two subsets of ℝ is ‘not’ the union of their closures. The dual situation, involving the complement of the closure of the union, is investigated constructively, using completeness of the ambient space in order to avoid any application of Markov's Principle.
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  18.  13
    Uniform Continuity Properties of Preference Relations.Douglas S. Bridges - 2008 - Notre Dame Journal of Formal Logic 49 (1):97-106.
    The anti-Specker property, a constructive version of sequential compactness, is used to prove constructively that a pointwise continuous, order-dense preference relation on a compact metric space is uniformly sequentially continuous. It is then shown that Ishihara's principle BD-ℕ implies that a uniformly sequentially continuous, order-dense preference relation on a separable metric space is uniformly continuous. Converses of these two theorems are also proved.
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  19.  18
    A Criterion for Compactness in Metric Spaces?Douglas S. Bridges - 1979 - Mathematical Logic Quarterly 25 (7‐12):97-98.
  20.  24
    A Criterion for Compactness in Metric Spaces?Douglas S. Bridges - 1979 - Mathematical Logic Quarterly 25 (7-12):97-98.
  21.  9
    A General Constructive Intermediate Value Theorem.Douglas S. Bridges - 1989 - Mathematical Logic Quarterly 35 (5):433-435.
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  22.  22
    A General Constructive Intermediate Value Theorem.Douglas S. Bridges - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (5):433-435.
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  23.  9
    Almost new pre-apartness from old.Douglas S. Bridges - 2012 - Annals of Pure and Applied Logic 163 (8):1009-1015.
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  24.  17
    Apartness spaces and uniform neighbourhood structures.Douglas S. Bridges - 2016 - Annals of Pure and Applied Logic 167 (9):850-864.
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  25.  22
    Characterising dominated weak-operator continuous functionals on subspaces of B.Douglas S. Bridges - 2013 - Annals of Pure and Applied Logic 164 (4):416-420.
    A characterisation of a type of weak-operator continuous linear functional on certain linear subsets of B, where H is a Hilbert space, is derived within Bishop-style constructive mathematics.
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  26.  14
    Constructing local optima on a compact interval.Douglas S. Bridges - 2007 - Archive for Mathematical Logic 46 (2):149-154.
    The existence of either a maximum or a minimum for a uniformly continuous mapping f of a compact interval into ${\mathbb{R}}$ is established constructively under the hypotheses that f′ is sequentially continuous and f has at most one critical point.
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  27.  13
    Constructive notions of strict convexity.Douglas S. Bridges - 1993 - Mathematical Logic Quarterly 39 (1):295-300.
    Two classically equivalent, but constructively inequivalent, strict convexity properties of a preference relation are discussed, and conditions given under which the stronger notion is a consequence of the weaker. The last part of the paper introduces uniformly rotund preferences, and shows that uniform rotundity implies strict convexity. The paper is written from a strictly constructive point of view, in which all proofs embody algorithms. MSC: 03F60, 90A06.
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  28.  2
    Constructive Solutions of Ordinary Differential Equations.Douglas S. Bridges - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter. pp. 67-78.
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  29.  6
    First steps in constructive game theory.Douglas S. Bridges - 2004 - Mathematical Logic Quarterly 50 (4-5):501-506.
    The minimax theorem of matrix game theory is examined from a constructive point of view. It is then shown that the existence of solutions for matrix games cannot be proved constructively, but that a 2-by-2 game with at most one solution has a constructible solution.
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  30.  31
    Geometric Intuition and Elementary Constructive Analysis.Douglas S. Bridges - 1979 - Mathematical Logic Quarterly 25 (33):521-523.
  31.  6
    On the Constructive Convergence of Series of Independent Functions.Douglas S. Bridges - 1979 - Mathematical Logic Quarterly 25 (3‐6):93-96.
  32.  27
    On the Constructive Convergence of Series of Independent Functions.Douglas S. Bridges - 1979 - Mathematical Logic Quarterly 25 (3-6):93-96.
  33.  19
    Sequential, pointwise, and uniform continuity: A constructive note.Douglas S. Bridges - 1993 - Mathematical Logic Quarterly 39 (1):55-61.
    The main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real-valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.
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  34.  23
    Square roots and powers in constructive banach algebra theory.Douglas S. Bridges & Robin S. Havea - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 68--77.
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  35.  27
    The Continuum Hypothesis Implies Excluded Middle.Douglas S. Bridges - 2016 - In Peter Schuster & Dieter Probst (eds.), Concepts of Proof in Mathematics, Philosophy, and Computer Science. Boston: De Gruyter. pp. 111-114.
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  36.  10
    Constructive Analysis.Errett Bishop & Douglas S. Bridges - 1985 - Berlin, Heidelberg, New York, and Tokyo: Springer.
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  37.  21
    Continuity properties of preference relations.Marian A. Baroni & Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (5):454-459.
    Various types of continuity for preference relations on a metric space are examined constructively. In particular, necessary and sufficient conditions are given for an order-dense, strongly extensional preference relation on a complete metric space to be continuous. It is also shown, in the spirit of constructive reverse mathematics, that the continuity of sequentially continuous, order-dense preference relations on complete, separable metric spaces is connected to Ishihara's principleBD-ℕ, and therefore is not provable within Bishop-style constructive mathematics alone.
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  38.  18
    Constructive Mathematics in Theory and Programming Practice.Douglas Bridges & Steeve Reeves - 1998 - Philosophia Mathematica 6 (3):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics. it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
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  39.  92
    Constructive mathematics in theory and programming practice.Douglas Bridges & Steeve Reeves - 1999 - Philosophia Mathematica 7 (1):65-104.
    The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop's constructive mathematics (BISH). it gives a sketch of both Myhill's axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focusses on the relation between constructive mathematics and programming, with emphasis on Martin-L6f 's theory of types as a formal system for BISH.
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  40.  32
    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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  41.  22
    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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  42.  22
    A Definitive Constructive Open Mapping Theorem?Douglas Bridges & Hajime Ishihara - 1998 - Mathematical Logic Quarterly 44 (4):545-552.
    It is proved, within Bishop's constructive mathematics , that, in the context of a Hilbert space, the Open Mapping Theorem is equivalent to a principle that holds in intuitionistic mathematics and recursive constructive mathematics but is unlikely to be provable within BISH.
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  43.  14
    A Weak Constructive Sequential Compactness Property And The Fan Theorem.Douglas Bridges - 2005 - Logic Journal of the IGPL 13 (2):151-158.
    A weak constructive sequential compactness property of metric spaces is introduced. It is proved that for complete, totally bounded metric spaces this property is equivalent to Brouwer's fan theorem for detachable bars. Our results form a part of constructive reverse mathematics.
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  44.  12
    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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  45.  12
    Sequential Continuity of Functions in Constructive Analysis.Douglas Bridges & Ayan Mahalanobis - 2000 - Mathematical Logic Quarterly 46 (1):139-143.
    It is shown that in any model of constructive mathematics in which a certain omniscience principle is false, for strongly extensional functions on an interval the distinction between sequentially continuous and regulated disappears. It follows, without the use of Markov's Principle, that any recursive function of bounded variation on a bounded closed interval is recursively sequentially continuous.
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  46.  27
    The anti-Specker property, a Heine–Borel property, and uniform continuity.Josef Berger & Douglas Bridges - 2008 - Archive for Mathematical Logic 46 (7-8):583-592.
    Working within Bishop’s constructive framework, we examine the connection between a weak version of the Heine–Borel property, a property antithetical to that in Specker’s theorem in recursive analysis, and the uniform continuity theorem for integer-valued functions. The paper is a contribution to the ongoing programme of constructive reverse mathematics.
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  47.  8
    Constructive aspects of Riemann’s permutation theorem for series.J. Berger, Douglas Bridges, Hannes Diener & Helmet Schwichtenberg - forthcoming - Logic Journal of the IGPL.
    The notions of permutable and weak-permutable convergence of a series|$\sum _{n=1}^{\infty }a_{n}$|of real numbers are introduced. Classically, these two notions are equivalent, and, by Riemann’s two main theorems on the convergence of series, a convergent series is permutably convergent if and only if it is absolutely convergent. Working within Bishop-style constructive mathematics, we prove that Ishihara’s principle BD-|$\mathbb {N}$|implies that every permutably convergent series is absolutely convergent. Since there are models of constructive mathematics in which the Riemann permutation theorem for (...)
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  48.  54
    Proceedings of the 4th World Conference on Research Integrity: Brazil, Rio de Janeiro. 31 May - 3 June 2015.Lex Bouter, Melissa S. Anderson, Ana Marusic, Sabine Kleinert, Susan Zimmerman, Paulo S. L. Beirão, Laura Beranzoli, Giuseppe Di Capua, Silvia Peppoloni, Maria Betânia de Freitas Marques, Adriana Sousa, Claudia Rech, Torunn Ellefsen, Adele Flakke Johannessen, Jacob Holen, Raymond Tait, Jillon Van der Wall, John Chibnall, James M. DuBois, Farida Lada, Jigisha Patel, Stephanie Harriman, Leila Posenato Garcia, Adriana Nascimento Sousa, Cláudia Maria Correia Borges Rech, Oliveira Patrocínio, Raphaela Dias Fernandes, Laressa Lima Amâncio, Anja Gillis, David Gallacher, David Malwitz, Tom Lavrijssen, Mariusz Lubomirski, Malini Dasgupta, Katie Speanburg, Elizabeth C. Moylan, Maria K. Kowalczuk, Nikolas Offenhauser, Markus Feufel, Niklas Keller, Volker Bähr, Diego Oliveira Guedes, Douglas Leonardo Gomes Filho, Vincent Larivière, Rodrigo Costas, Daniele Fanelli, Mark William Neff, Aline Carolina de Oliveira Machado Prata, Limbanazo Matandika, Sonia Maria Ramos de Vasconcelos & Karina de A. Rocha - 2016 - Research Integrity and Peer Review 1 (Suppl 1).
    Table of contentsI1 Proceedings of the 4th World Conference on Research IntegrityConcurrent Sessions:1. Countries' systems and policies to foster research integrityCS01.1 Second time around: Implementing and embedding a review of responsible conduct of research policy and practice in an Australian research-intensive universitySusan Patricia O'BrienCS01.2 Measures to promote research integrity in a university: the case of an Asian universityDanny Chan, Frederick Leung2. Examples of research integrity education programmes in different countriesCS02.1 Development of a state-run “cyber education program of research ethics” in (...)
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  49.  48
    Bridging the Gap: From Cognitive Anthropology to Cognitive Science.Andrea Bender, Sieghard Beller, Giovanni Bennardo, James S. Boster, Asifa Majid & Douglas L. Medin - 2010 - In S. Ohlsson & R. Catrambone (eds.), Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Cognitive Science Society.
  50.  6
    Merleau-Ponty's Last Vision: A Proposal for the Completion of the Visible and the Invisible.Douglas Beck Low - 2000 - Evanston, Ill.: Northwestern University Press.
    Few writers' unfinished works are considered among their most important, but such is the case with Merleau-Ponty's _The Visible and the Invisible_. What exists of it is a mere beginning, yet it bridged modernism and postmodernism in philosophy. Low uses material from some of Merleau-Ponty's later works as the basis for completion. Working from this material and the philosopher's own outline, Low presents how this important work would have looked had Merleau-Ponty lived to complete it.
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