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

@inproceedings{Hamilton1999ToposPO,
  title={Topos Perspective on the Kochen-Specker Theorem : III . Von Neumann Algebras as the Base Category},
  author={J Michael Hamilton and C. J. Isham},
  year={1999}
}
We extend the topos-theoretic treatment given in previous papers [1, 2] 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).