Conditions that Force an Orthomodular Poset to Be a Boolean Algebra
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Tkadlec, Josef
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We introduce two new classes of orthomodular posets—the class
of weakly Boolean orthomodular posets and the class of orthomodular posets
with the property of maximality. The main result of this paper is that the intersection
of these classes is the class of Boolean algebras. Since the first class
introduced here contains various classes of orthomodular posets with a given
property of its state space and the second class contains, e.g., lattice (orthocomplete,
resp.) orthomodular posets, the main theorem can be viewed as a
generalization of various results concerning the question when an orthomodular
poset has to be a Boolean algebra. Moreover, it gives alternative proofs to
previous results and new results of this type.
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