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Cut-Elimination: Syntax and Semantics

Studia Logica 102 (6):1217-1244 (2014)

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  1. Gentzen’s “cut rule” and quantum measurement in terms of Hilbert arithmetic. Metaphor and understanding modeled formally.Vasil Penchev - 2022 - Logic and Philosophy of Mathematics eJournal 14 (14):1-37.
    Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...)
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  • Ceres in intuitionistic logic.David Cerna, Alexander Leitsch, Giselle Reis & Simon Wolfsteiner - 2017 - Annals of Pure and Applied Logic 168 (10):1783-1836.
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