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  1. Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
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  • al-Akhlāq: uṣūluhā al-dīnīyah wa-judhūruhā al-falsafīyah.Muḥammad ʻAlī Bārr - 2010 - Jiddah: Kursī Akhlāqīyāt al-Ṭibb.
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  • The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
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  • A topos perspective on the kochen-Specker theorem: I. Quantum states as generalised valuations.Chris Isham & Jeremy Butterfield - unknown
    Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context (...)
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  • From absolute to local mathematics.J. L. Bell - 1986 - 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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  • Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
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  • Boolean models and nonstandard analysis.Dana Scott - 1969 - In W. A. J. Luxemburg (ed.), Applications of model theory to algebra, analysis, and probability. New York,: Holt, Rinehart and Winston. pp. 87--92.
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  • Background Independence in Quantum Gravity and Forcing Constructions.Jerzy Król - 2004 - Foundations of Physics 34 (3):361-403.
    A general duality connecting the level of a formal theory and of a metatheory is proposed. Because of the role of natural numbers in a metatheory the existence of a dual theory is conjectured, in which the natural numbers become formal in the theory but in formalizing non-formal natural numbers taken from the dual metatheory these numbers become nonstandard. For any formal theory there may be in principle a dual theory. The dual shape of the lattice of projections over separable (...)
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  • Towards a Coherent Theory of Physics and Mathematics.Paul Benioff - 2002 - Foundations of Physics 32 (7):989-1029.
    As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and (...)
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  • Orthospaces and quantum logic.J. L. Bell - 1985 - 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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  • Boolean-Valued Models and Independence Proofs in Set Theory.John Lane Bell - 1977 - Oxford, England: Clarendon Press.
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  • The Mathematics of Metamathematics.Donald Monk - 1963 - Journal of Symbolic Logic 32 (2):274-275.
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  • Exotic Smoothness and Noncommutative Spaces. The Model-Theoretical Approach.Jerzy Król - 2004 - Foundations of Physics 34 (5):843-869.
    We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial R4. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between ‘‘localized’’ exotic small R4’s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R4’s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means (...)
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  • Diagonalization of continuous matrices as a representation of intuitionistic reals.Andre Scedrov - 1986 - Annals of Pure and Applied Logic 30 (2):201-206.
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  • Set theory.Thomas Jech - 1981 - Journal of Symbolic Logic.
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  • Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity.C. J. Isham & J. Butterfield - 2000 - Foundations of Physics 30 (10):1707-1735.
    We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.
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  • Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1981 - Journal of Symbolic Logic 46 (1):165-165.
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  • Boolean-Valued Models and Independence Proofs in Set Theory.J. L. Bell & Dana Scott - 1986 - Journal of Symbolic Logic 51 (4):1076-1077.
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  • Feynman path integrals.Cécile DeWitt-Morette - 1984 - In Heinrich Mitter & Ludwig Pittner (eds.), Stochastic methods and computer techniques in quantum dynamics. New York: Springer Verlag. pp. 101--170.
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  • A topos perspective on the kochen-Specker theorem: II. Conceptual aspects, and classical analogues.Jeremy Butterfield & Chris Isham - unknown
    In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed valuations (...)
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  • Two applications of logic to mathematics.Gaisi Takeuti - 1978 - [Princeton, N.J.]: Princeton University Press.
    Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that (...)
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