16 found
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  1.  8
    Intuitionism As Generalization.Fred Richman - 1990 - Philosophia Mathematica (1-2):124-128.
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  2.  20
    The Kripke Schema in Metric Topology.Robert Lubarsky, Fred Richman & Peter Schuster - 2012 - Mathematical Logic Quarterly 58 (6):498-501.
    A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.
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  3.  12
    Intuitionistic Notions of Boundedness in ℕ.Fred Richman - 2009 - Mathematical Logic Quarterly 55 (1):31-36.
    We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most (...)
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  4.  11
    Stabilité En Théorie des Modèles.Daniel Lascar, Ray Mines, Fred Richman & Wim Ruitenburg - 1990 - Journal of Symbolic Logic 55 (2):883-886.
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  5.  49
    Linear Independence Without Choice.Douglas Bridges, Fred Richman & Peter Schuster - 1999 - Annals of Pure and Applied Logic 101 (1):95-102.
    The notions of linear and metric independence are investigated in relation to the property: if U is a set of n+1 independent vectors, and X is a set of n independent vectors, then adjoining some vector in U to X results in a set of n+1 independent vectors. It is shown that this property holds in any normed linear space. A related property – that finite-dimensional subspaces are proximinal – is established for strictly convex normed spaces over the real or (...)
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  6.  29
    Gleason's Theorem has a Constructive Proof.Fred Richman - 2000 - Journal of Philosophical Logic 29 (4):425-431.
    Gleason's theorem for ³ says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x, y, z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason's theorem in light of the recent publication of such a proof.
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  7.  45
    Church's Thesis Without Tears.Fred Richman - 1983 - Journal of Symbolic Logic 48 (3):797-803.
  8.  22
    Omniscience Principles and Functions of Bounded Variation.Fred Richman - 2002 - Mathematical Logic Quarterly 48 (1):111-116.
    A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function with located variation on an interval is the difference of two increasing functions.
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  9.  73
    Review of P. Fletcher, Truth, Proof and Infinity: A Theory of Constructive Reasoning.Fred Richman - 2000 - Philosophia Mathematica 8 (2):214-220.
  10.  9
    Real Numbers and Other Completions.Fred Richman - 2008 - Mathematical Logic Quarterly 54 (1):98-108.
    A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete Archimedean Heyting field, a terminal object in the category of Archimedean Heyting fields.
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  11.  36
    Nick Haverkamp. Intuitionism Vs. Classicism: A Mathematical Attack on Classical Logic. Studies in Theoretical Philosophy, Vol. 2. Frankfurt: Klostermann, 2015. ISBN 978-3-465-03906-8 . Pp. Xvi + 270. [REVIEW]Fred Richman - 2016 - Philosophia Mathematica 24 (2):278-278.
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  12.  44
    Equivalence of Syllogisms.Fred Richman - 2004 - Notre Dame Journal of Formal Logic 45 (4):215-233.
    We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. For a more natural development, using group-theoretic methods, the space of syllogisms is enlarged to include nonstandard syllogisms, and various groups of transformations (...)
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  13.  9
    Bridges D. S.. Constructive Functional Analysis. Research Notes in Mathematics, No. 28. Pitman Publishing, London, San Francisco, and Melbourne, 1979, Iv + 203 Pp.Zahn Peter. Ein Konstruktiver Weg Zur Masstheorie Und Funktionalanalysis. Wissenschaftliche Buchgesellschaft, Darmstadt 1978, 350 Pp. [REVIEW]Fred Richman - 1982 - Journal of Symbolic Logic 47 (3):703-705.
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  14.  16
    Review of A. S. Troelstra and D. Van Dalen, Constructivism in Mathematics: An Introduction[REVIEW]Fred Richman - 1994 - Philosophia Mathematica 2 (1):86-89.
  15.  3
    Review of C. Ormell, Some Criteria for Set in Mathematics[REVIEW]Fred Richman - 1997 - Philosophia Mathematica 5 (1).
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  16. Constructive Mathematics: Proceedings of the New Mexico State University Conference Held at Las Cruces, New Mexico, August 11-15, 1980. [REVIEW]Fred Richman (ed.) - 1981 - Springer Verlag.