Maximal structures of determinate propositions in quantum mechanics

I formulate and answer some questions concerning maximal structures of determinate quantum propositions, i.e., maximal structures of propositions that can be taken as having definite (but perhaps unknown) truth values for a given quantum state. The basic constraint on such structures is the Kochen and Specker no-go hidden-variables theorem, which demonstrates that no value assignment to certain finite sets of observables can preserve the functional relations between commuting observables. The problem I want to consider is how large we can take the set of determinate observables without violating the functional relationship constraint. I show how to construct maximal determinate sublattices of quantum propositions that are unique, subject to certain constraints, and I comment on the relevance of this go theorem for the interpretation of quantum mechanics.