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On the set representation of an orthomodular poset
2001
Colloquium Mathematicum
Let P be an orthomodular poset and let B be a Boolean subalgebra of P . A mapping s : P → 0, 1 is said to be a centrally additive B-state if it is order preserving, satisfies s(a ′ ) = 1 − s(a), is additive on couples that contain a central element, and restricts to a state on B. It is shown that, for any Boolean subalgebra B of P , P has an abundance of two-valued centrally additive B-states. This answers positively a question raised in [13, Open question, p. 13]. As a consequence one obtains
doi:10.4064/cm89-2-8
fatcat:fauu4xvoprd3zbnu2qhle4m5fe