Concrete quantum logics with generalised compatibility

Josef Tkadlec

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 2, page 213-218
  • ISSN: 0862-7959

Abstract

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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].

How to cite

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Tkadlec, Josef. "Concrete quantum logics with generalised compatibility." Mathematica Bohemica 123.2 (1998): 213-218. <http://eudml.org/doc/248303>.

@article{Tkadlec1998,
abstract = {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].},
author = {Tkadlec, Josef},
journal = {Mathematica Bohemica},
keywords = {orthomodular poset; concrete quantum logic; Boolean algebra; covering; Jauch-Piron state; orthocompleteness; orthomodular poset; concrete quantum logic; Boolean algebra},
language = {eng},
number = {2},
pages = {213-218},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Concrete quantum logics with generalised compatibility},
url = {http://eudml.org/doc/248303},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Tkadlec, Josef
TI - Concrete quantum logics with generalised compatibility
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 2
SP - 213
EP - 218
AB - 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].
LA - eng
KW - orthomodular poset; concrete quantum logic; Boolean algebra; covering; Jauch-Piron state; orthocompleteness; orthomodular poset; concrete quantum logic; Boolean algebra
UR - http://eudml.org/doc/248303
ER -

References

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  1. S. P. Gudder, Stochastic Methods in Quantum Mechanics, North Holland, New York, 1979. (1979) Zbl0439.46047MR0543489
  2. V. Müller, 10.1007/BF00673353, Int. J. Theor. Phys. 32 (1993), 433-442. (1993) MR1213098DOI10.1007/BF00673353
  3. V. Müller P. Pták J. Tkаdlec, 10.1007/BF00678549, Int. J. Theor. Phys. 31 (1992), 843-854. (1992) MR1162627DOI10.1007/BF00678549
  4. M. Nаvаrа P. Pták, 10.1016/0022-4049(89)90108-4, J. Pure Appl. Algebra 60 (1989), 105-111. (1989) MR1014608DOI10.1016/0022-4049(89)90108-4
  5. P. Pták, Some nearly Boolean orthomodular posets, Proc. Amer. Math. Soc. To appear. MR1452822
  6. P. Pták S. Pulmаnnová, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991. (1991) MR1176314
  7. J. Tkаdlec, Boolean orthoposets-concreteness and orthocompleteness, Math. Bohem. 119 (1994), 123-128. (1994) MR1293244
  8. J. Tkаdlec, Conditions that force an orthomodular poset to be a Boolean algebra, Tatra Mt. Math. Publ. 10 (1997), 55-62. (1997) MR1469281

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