Topos Perspective on the Kochen=nSpeckerTheorem: III. Von Neumann Algebras as theBase Category

@article{Hamilton1999ToposPO,
title={Topos Perspective on the Kochen=nSpeckerTheorem: III. Von Neumann Algebras as theBase Category},
author={J. Hamilton and C. Isham and J. Butterfield},
journal={International Journal of Theoretical Physics},
year={1999},
volume={39},
pages={1413-1436}
}

We extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as theKochen–Specker theorem. This extension has two main parts: the use of vonNeumann algebras as a base category and the relation of our generalized valuationsto (i) the assignment to quantities of intervals of real numbers and (ii) the ideaof a subobject of the coarse-graining presheaf.