| 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:
|
http://hdl.handle.net/10338.dmlcz/126300 |
| . |
| 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 |
| . |
