Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem

Hrushovski, Ehud and Pitowsky, Itamar (2003) Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem.

Abstract

Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.