GREECHIE DIAGRAMS, NONEXISTENCE OF MEASURES IN QUANTUM-LOGICS, AND KOCHEN-SPECKER-TYPE CONSTRUCTIONS

We use Greechie diagrams to construct finite orthomodular lattices ''r ealizable'' in the orthomodular lattice of subspaces in a three-dimens ional Hilbert space such that the set of two-valued states is not ''la rge'' (i.e., full, separating, unital, nonempty, resp.). We discuss th e number of elements of such orthomodular lattices, of their sets of ( ortho)generators and of their subsets that do not admit a ''large'' se t of two-valued states. We show connections with other results of this type. (C) 1996 American Institute of Physics.