@Article{Navara:INS09, IS = { zkontrolovano 21 Jan 2010 }, UPDATE = { 2009-12-29 }, author = {Navara, Mirko}, title = {Existence of states on quantum structures}, year = {2009}, month = {February}, pages = {508--514}, journal = {Information Sciences}, publisher = {Elsevier}, address = {Amsterdam, Netherlands}, issn = {0020-0255}, volume = {179}, number = {5}, annote = {Orthomodular lattices occurred as generalized event structures in the models of probability for quantum mechanics. Here we contribute to the question of existence of states (=probability measures) on orthomodular lattices. We prove that known techniques do not allow to find examples with less than 19~blocks (=maximal Boolean subalgebras). This bound is achieved by the example by R.~Mayet. Although we do not finally exclude the existence of other techniques breaking this bound, existence of smaller examples is highly unexpected.}, keywords = {orthomodular lattice, quantum logic, state, probability measure, block, Boolean subalgebra, pasting}, project = {GACR 201/07/1051}, psurl = {DOI 10.1016/j.ins.2008.06.011}, }