Some nearly Boolean orthomodular posets

Pták, Pavel

doi:10.1090/S0002-9939-98-04403-7

Some nearly Boolean orthomodular posets
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Proc. Amer. Math. Soc. 126 (1998), 2039-2046 Request permission

Abstract:

Let $L$ be an orthomodular partially ordered set (“a quantum logic"). Let us say that $L$ is nearly Boolean if $L$ is set-representable and if every state on $L$ is subadditive. We first discuss conditions under which a nearly Boolean OMP must be Boolean. Then we show that in general a nearly Boolean OMP does not have to be Boolean. Moreover, we prove that an arbitrary Boolean algebra may serve as the centre of a (non-Boolean) nearly Boolean OMP.

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