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  1. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (forthcoming). Intuitionistic Quantum Logic for von Neumann Algebras. Synthese.
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  2. Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2012). Bohrification of Operator Algebras and Quantum Logic. Synthese 186 (3):719 - 752.
    Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...)
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  3. Bas Spitters (2012). The Space of Measurement Outcomes as a Spectral Invariant for Non-Commutative Algebras. Foundations of Physics 42 (7):896-908.
    The recently developed technique of Bohrification associates to a (unital) C*-algebra Athe Kripke model, a presheaf topos, of its classical contexts;in this Kripke model a commutative C*-algebra, called the Bohrification of A;the spectrum of the Bohrification as a locale internal in the Kripke model. We propose this locale, the ‘state space’, as a (n intuitionistic) logic of the physical system whose observable algebra is A.We compute a site which externally captures this locale and find that externally its points may be (...)
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  4. Thierry Coquand, Erik Palmgren & Bas Spitters (2011). Metric Complements of Overt Closed Sets. Mathematical Logic Quarterly 57 (4):373-378.
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  5. Bas Spitters (2010). Locatedness and Overt Sublocales. Annals of Pure and Applied Logic 162 (1):36-54.
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  6. Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2009). Intuitionistic Quantum Logic of an N-Level System. Foundations of Physics 39 (7):731-759.
    A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the (...)
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  7. Bas Spitters (2006). A Constructive View on Ergodic Theorems. Journal of Symbolic Logic 71 (2):611 - 623.
    Let T be a positive L₁-L∞ contraction. We prove that the following statements are equivalent in constructive mathematics. (1) The projection in L₂ on the space of invariant functions exists: (2) The sequence (Tⁿ)n∈N Cesáro-converges in the L₂ norm: (3) The sequence (Tⁿ)n∈N Cesáro-converges almost everywhere. Thus, we find necessary and sufficient conditions for the Mean Ergodic Theorem and the Dunford-Schwartz Pointwise Ergodic Theorem. As a corollary we obtain a constructive ergodic theorem for ergodic measure-preserving transformations. This answers a question (...)
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  8. Bas Spitters (2006). Corrigendum To: 'A Constructive View on Ergodic Theorems'. Journal of Symbolic Logic 71 (4):1431 - 1432.
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  9. Bas Spitters (2006). Constructive Algebraic Integration Theory. Annals of Pure and Applied Logic 137 (1):380-390.
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  10. Thierry Coquand & Bas Spitters (2005). A Constructive Proof of the Peter‐Weyl Theorem. Mathematical Logic Quarterly 51 (4):351-359.
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  11. Chris Heunen, Klaas Landsman & Bas Spitters, The Principle of General Tovariance.
    We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining (...)
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