Kochen-Specker Sets and Generalized Orthoarguesian Equations

Abstract

We prove that the 7oa class (equational variety) of generalized orthoarguesian lattices is properly included in all noa classes for n < 7. This result strengthens the conjecture that any generalized orthoarguesian equation is strictly stronger than those of lower orders. The result emerged from our recent analysis of whether three-dimensional Kochen-Specker sets can be represented by Greechie lattices, which are a kind of orthomodular lattice. © 2011 Springer Basel AG.