Orthomodular lattices with state-separated noncompatible pairs
نویسندگان
چکیده
منابع مشابه
Orthomodular Lattices with Rich State Spaces Orthomodular Lattices with Rich State Spaces
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 variet...
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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 variet...
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The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings – as a relationa...
متن کاملConstructions and Varieties of Orthomodular Lattices with Rich State Spaces
Among previous constructions of orthomodular lattices, there was a lack of techniques which enabled to obtain rich spaces of states (=probability measures). On the other side, from the point of view of quantum physics, the following requirement is essential: For each pair of incomparable elements a; c there is a state s such that s(a) = 1 > s(c). We found out a powerful tool for such constructi...
متن کاملSubalgebras of Orthomodular Lattices
Sachs (Can J Math 14:451–460, 1962) showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The domain BSub(L) has recently found use in an approach to the foundation...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2000
ISSN: 0011-4642,1572-9141
DOI: 10.1023/a:1022479104160