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  1. Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem.Itamar Pitowsky - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.
    Kochen and Specker’s theorem can be seen as a consequence of Gleason’s theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason’s theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated. r 2003 Elsevier Ltd. All rights reserved.
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  • Quantum Logic and the Classical Propositional Calculus.Othman Qasim Malhas - 1987 - Journal of Symbolic Logic 52 (3):834-841.
    In much the same way that it is possible to construct a model of hyperbolic geometry in the Euclidean plane, it is possible to model quantum logic within the classical propositional calculus.
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  • Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem.Ehud Hrushovski & Itamar Pitowsky - 2004 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35 (2):177-194.
    Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.
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  • Generalization of the Greenberger-Horne-Zeilinger Algebraic Proof of Nonlocality.Robert K. Clifton, Michael L. G. Redhead & Jeremy N. Butterfield - 1991 - Foundations of Physics 21 (2):149-184.
    We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument be modified (...)
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