A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category

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Hamilton, John; Isham, Chris; Butterfield, Jeremy
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We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem. This extension has two main parts: the use of von Neumann algebras as a base category (Section 2); and the relation of our generalized valuations to (i) the assignment to quantities of intervals of real numbers, and (ii) the idea of a subobject of the coarse-graining presheaf (Section 3).