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  1. Sheaves and Logic.M. P. Fourman, D. S. Scott & C. J. Mulvey - 1983 - Journal of Symbolic Logic 48 (4):1201-1203.
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  • Sublocales in Formal Topology.Steven Vickers - 2007 - Journal of Symbolic Logic 72 (2):463 - 482.
    The paper studies how the localic notion of sublocale transfers to formal topology. For any formal topology (not necessarily with positivity predicate) we define a sublocale to be a cover relation that includes that of the formal topology. The family of sublocales has set-indexed joins. For each set of base elements there are corresponding open and closed sublocales, boolean complements of each other. They generate a boolean algebra amongst the sublocales. In the case of an inductively generated formal topology, the (...)
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  • Partial Horn logic and cartesian categories.Erik Palmgren & Steven J. Vickers - 2007 - Annals of Pure and Applied Logic 145 (3):314-353.
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  • The principle of general tovariance.Chris Heunen, Klaas Landsman & Bas Spitters - unknown
    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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  • A localic theory of lower and upper integrals.Steven Vickers - 2008 - Mathematical Logic Quarterly 54 (1):109-123.
    An account of lower and upper integration is given. It is constructive in the sense of geometric logic. If the integrand takes its values in the non-negative lower reals, then its lower integral with respect to a valuation is a lower real. If the integrand takes its values in the non-negative upper reals, then its upper integral with respect to a covaluation and with domain of integration bounded by a compact subspace is an upper real. Spaces of valuations and of (...)
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  • Cosheaves and connectedness in formal topology.Steven Vickers - 2012 - Annals of Pure and Applied Logic 163 (2):157-174.
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