Abstract:We introduce a new construction technique for orthomodular lattices. In contrast to the preceding constructions, it admits rich spaces of states (= probability measures), i.e., for each pair of incomparable elements a, c there is a state s such that s(a) = 1 > s(c). This allowed a progress in many questions that were open for a long time; among others we prove that there is a continuum of varieties of orthomodular lattices with rich state spaces and solve a problem formulated by R. Mayet in 1985. As a by-produ… Show more
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