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We show that the variety of ortholattices has the strong amalgamation property and that the variety of orthomodular lattices has the strong Boolean amalgamation property, i.e. that two orthomodular lattices can be strongly amalgamated over a common Boolean subalgebra. We give examples to show that the variety orthomodular lattices does not have the amalgamation property and that the variety of modular ortholattices does not even have the Boolean amalgamation property. We further show that no non-Boolean variety of orthomodular lattices which is generated by orthomodular lattices of bounded height can have the Boolean amalgamation property. 相似文献
2.
Ivan Chajda 《Czechoslovak Mathematical Journal》2008,58(1):15-21
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization
of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
This work is supported by the Research Project MSM 6198959214 by Czech Goverment. 相似文献
3.
We involve a certain propositional logic based on an ortholattice. We characterize the implication reduct of such a logic
and show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence kernels
of these algebras are described.
This article was prepared under the support of Czech Government Council No. 314/98:153100011.
MS classification: 06C15, 03G25, 08A30 相似文献
4.
We prove that on every separable complete atomic modular ortholattice (i.e.order topological) there exists an order continuous faithful valuation. We also give a construction of the existing order continuous faithful valuation. For separable atomic modular ortholattices we give a necessary and sufficient condition to admit an order continuous faithful valuation and we show that it is equivalent with the condition to have a modular MacNeille completion. We improve one statement on complete metric lattices from Birkhoff's Lattice Theory.
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We prove a lemma which, under restrictive conditions, shows that epimorphisms in V are surjective if this is true for epimorphisms from irreducible members of V. This lemma is applied to varieties of orthomodular lattices which are generated by orthomodular lattices of bounded height, and to varieties of orthomodular lattices which are generated by orthomodular lattices which are the horizontal sum of their blocks. The lemma can also be applied to obtain known results for discriminator varieties. 相似文献
6.
Simple Axioms for Orthomodular Implication Algebras 总被引:1,自引:0,他引:1
Ivan Chajda Radomír Halaš Helmut Länger 《International Journal of Theoretical Physics》2004,43(4):911-914
Simple, independent axioms for orthomodular implication algebras are presented. 相似文献
7.
In their 1936 founding paper on quantum logic, Birkhoff and von Neumann postulated that the lattice describing the experimental
propositions concerning a quantum system is orthocomplemented. We prove that this postulate fails for the lattice
sep describing a compound system consisting of so called separated quantum systems. By separated we mean two systems prepared in different “rooms” of the lab, and before any interaction takes
place. In that case, the state of the compound system is necessarily a product state. As a consequence, Dirac’s superposition
principle fails, and therefore
sep cannot satisfy all Piron’s axioms. In previous works, assuming that
sep is orthocomplemented, it was argued that
sep is not orthomodular and fails to have the covering property. Here we prove that
sep cannot admit an orthocomplementation. Moreover, we propose a natural model for
sep which has the covering property.
PACS: 03.65.Ta, 03.65.Ca 相似文献
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