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Title: Concrete quantum logics with generalised compatibility (English)
Author: Tkadlec, Josef
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 123
Issue: 2
Year: 1998
Pages: 213-218
Summary lang: English
Category: math
Summary: We present three results stating when a concrete (=set-representable) quantum logic with covering properties (generalization of compatibility) has to be a Boolean algebra. These results complete and generalize some previous results [3, 5] and answer partiallz a question posed in [2]. (English)
Keyword: orthomodular poset
Keyword: concrete quantum logic
Keyword: Boolean algebra
Keyword: covering
Keyword: Jauch-Piron state
Keyword: orthocompleteness
MSC: 03G12
MSC: 06C15
MSC: 81P10
idZBL: Zbl 0938.03093
idMR: MR1673973
DOI: 10.21136/MB.1998.126300
Date available: 2009-09-24T21:30:58Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] S. P. Gudder: Stochastic Methods in Quantum Mechanics.North Holland, New York, 1979. Zbl 0439.46047, MR 0543489
Reference: [2] V. Müller: Jauch-Piron states on concrete quantum logics.Int. J. Theor. Phys. 32 (1993), 433-442. MR 1213098, 10.1007/BF00673353
Reference: [3] V. Müller P. Pták J. Tkаdlec: Concrete quantum logics with covering properties.Int. J. Theor. Phys. 31 (1992), 843-854. MR 1162627, 10.1007/BF00678549
Reference: [4] M. Nаvаrа P. Pták: Almost Boolean orthomodular posets.J. Pure Appl. Algebra 60 (1989), 105-111. MR 1014608, 10.1016/0022-4049(89)90108-4
Reference: [5] P. Pták: Some nearly Boolean orthomodular posets.Proc. Amer. Math. Soc. To appear. MR 1452822
Reference: [6] P. Pták S. Pulmаnnová: Orthomodular Structures as Quantum Logics.Kluwer, Dordrecht, 1991. MR 1176314
Reference: [7] J. Tkаdlec: Boolean orthoposets-concreteness and orthocompleteness.Math. Bohem. 119 (1994), 123-128. MR 1293244
Reference: [8] J. Tkаdlec: Conditions that force an orthomodular poset to be a Boolean algebra.Tatra Mt. Math. Publ. 10 (1997), 55-62. MR 1469281


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