Abstract
Let L L be an orthomodular partially ordered set (“a quantum logic"). Let us say that L L is nearly Boolean if L L is set-representable and if every state on L 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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