Concrete quantum logics with generalised compatibility
Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 213-218

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MR Zbl
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].
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].
DOI : 10.21136/MB.1998.126300
Classification : 03G12, 06C15, 81P10
Keywords: orthomodular poset; concrete quantum logic; Boolean algebra; covering; Jauch-Piron state; orthocompleteness
Tkadlec, Josef. Concrete quantum logics with generalised compatibility. Mathematica Bohemica, Tome 123 (1998) no. 2, pp. 213-218. doi: 10.21136/MB.1998.126300
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[1] S. P. Gudder: Stochastic Methods in Quantum Mechanics. North Holland, New York, 1979. | MR | Zbl

[2] V. Müller: Jauch-Piron states on concrete quantum logics. Int. J. Theor. Phys. 32 (1993), 433-442. | DOI | MR

[3] V. Müller P. Pták J. Tkаdlec: Concrete quantum logics with covering properties. Int. J. Theor. Phys. 31 (1992), 843-854. | DOI | MR

[4] M. Nаvаrа P. Pták: Almost Boolean orthomodular posets. J. Pure Appl. Algebra 60 (1989), 105-111. | DOI | MR

[5] P. Pták: Some nearly Boolean orthomodular posets. Proc. Amer. Math. Soc. To appear. | MR

[6] P. Pták S. Pulmаnnová: Orthomodular Structures as Quantum Logics. Kluwer, Dordrecht, 1991. | MR

[7] J. Tkаdlec: Boolean orthoposets-concreteness and orthocompleteness. Math. Bohem. 119 (1994), 123-128. | MR

[8] J. Tkаdlec: Conditions that force an orthomodular poset to be a Boolean algebra. Tatra Mt. Math. Publ. 10 (1997), 55-62. | MR

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