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  1. J. L. Bell, A Geometric Form of the Axiom of Choice.
    Consider the following well-known result from the theory of normed linear spaces ([2], p. 80, 4(b)): (g) the unit ball of the (continuous) dual of a normed linear space over the reals has an extreme point. The standard proof of (~) uses the axiom of choice (AG); thus the implication AC~(w) can be proved in set theory. In this paper we show that this implication can be reversed, so that (*) is actually eq7I2valent to the axiom of choice. From this (...)
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  2. J. L. Bell (2013). Review of M. Van Atten, P. Boldini, M. Bourdeau, and G. Heinzmann (Eds.), _One Hundred Years of Intuitionism (1907–2007): The Cerisy Conference. [REVIEW] Philosophia Mathematica 21 (3):392-399.
  3. J. L. Bell (2007). A. Kock, Synthetic Differential Geometry. Bulletin of Symbolic Logic 13 (2):244.
     
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  4. J. L. Bell (1997). Zorn's Lemma and Complete Boolean Algebras in Intuitionistic Type Theories. Journal of Symbolic Logic 62 (4):1265-1279.
    We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some (...)
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  5. J. L. Bell (1995). Review of B. Rotman, Ad Infinitum - The Ghost In Turing's Machine: Taking God Out of Mathematics and Putting the Body Back In: An Essay in Corporeal Semiotics. [REVIEW] Philosophia Mathematica 3 (2):218-221.
  6. J. L. Bell (1995). Type Reducing Correspondences and Well-Orderings: Frege's and Zermelo's Constructions Re-Examined. Journal of Symbolic Logic 60 (1):209-221.
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  7. J. L. Bell (1994). Introduction. Philosophia Mathematica 2 (1):4-4.
    Continuous as the stars that shine And twinkle on the milky way, They stretched in never-ending line Along the margin of a bay: Ten thousand saw I at a glance, Tossing their heads in sprightly dance.
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  8. J. L. Bell (1993). Hilbert's Ɛ-Operator and Classical Logic. Journal of Philosophical Logic 22 (1):1 - 18.
  9. J. L. Bell (1993). Review: Colin McLarty, Elementary Categories, Elementary Toposes. [REVIEW] Journal of Symbolic Logic 58 (3):1075-1076.
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  10. J. L. Bell (1989). Aczel Peter. Non-Well-Founded Sets. With a Foreword by Jon Barwise. CSLI Lecture Notes, No. 14. Center for the Study of Language and Information, Stanford 1988, Also Distributed by the University of Chicago Press, Chicago, Xx+ 131 Pp. [REVIEW] Journal of Symbolic Logic 54 (3):1111-1114.
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  11. J. L. Bell (1989). Review: J. Lambek, P. J. Scott, Introduction to Higher Order Categorical Logic. [REVIEW] Journal of Symbolic Logic 54 (3):1113-1114.
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  12. J. L. Bell & Hao Wang (1989). Reflections on Kurt Godel. Philosophical Quarterly 39 (154):115.
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  13. J. L. Bell (1988). Infinitesimals. Synthese 75 (3):285 - 315.
    The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...)
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  14. J. L. Bell & S. Feferman (1987). Collected Works of Kurt Godel: Volume I. Philosophical Quarterly 37 (147):216.
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  15. J. L. Bell (1986). A New Approach to Quantum Logic. British Journal for the Philosophy of Science 37 (1):83-99.
    The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical framework (...)
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  16. J. L. Bell (1986). From Absolute to Local Mathematics. Synthese 69 (3):409 - 426.
    In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.
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  17. J. L. Bell (1985). Orthospaces and Quantum Logic. Foundations of Physics 15 (12):1179-1202.
    In this paper we construct the ortholattices arising in quantum logic starting from the phenomenologically plausible idea of a collection of ensembles subject to passing or failing various “tests.” A collection of ensembles forms a certain kind of preordered set with extra structure called anorthospace; we show that complete ortholattices arise as canonical completions of orthospaces in much the same way as arbitrary complete lattices arise as canonical completions of partially ordered sets. We also show that the canonical completion of (...)
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  18. J. L. Bell (1983). On the Strength of the Sikorski Extension Theorem for Boolean Algebras. Journal of Symbolic Logic 48 (3):841-846.
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  19. J. L. Bell (1982). Categories, Toposes and Sets. Synthese 51 (3):293 - 337.
    This paper is an introduction to topos theory which assumes no prior knowledge of category theory. It includes a discussion of internal logic in a topos, A characterization of the category of sets, And an investigation of the notions of topology and sheaf in a topos.
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  20. J. L. Bell (1982). Reviews. [REVIEW] British Journal for the Philosophy of Science 33 (1):363-366.
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  21. J. L. Bell (1981). Category Theory and the Foundations of Mathematics. British Journal for the Philosophy of Science 32 (4):349-358.
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  22. J. L. Bell (1981). Isomorphism of Structures in s-Toposes. Journal of Symbolic Logic 46 (3):449-459.
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  23. J. L. Bell (1977). A Course in Mathematical Logic. Sole Distributors for the U.S.A. And Canada American Elsevier Pub. Co..
    A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.
     
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  24. J. L. Bell (1976). A Note on Generic Ultrafilters. Mathematical Logic Quarterly 22 (1):307-310.
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  25. J. L. Bell (1976). Universal Complete Boolean Algebras and Cardinal Collapsing. Mathematical Logic Quarterly 22 (1):161-164.
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  26. J. L. Bell (1975). Reviews. [REVIEW] British Journal for the Philosophy of Science 26 (2):363-366.
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  27. J. L. Bell (1974). On Compact Cardinals. Mathematical Logic Quarterly 20 (25‐27):389-393.
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  28. J. L. Bell (1972). Reviews. [REVIEW] British Journal for the Philosophy of Science 23 (4):363-366.
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