| Title:
|
Automorphisms of concrete logics (English) |
| Author:
|
Navara, Mirko |
| Author:
|
Tkadlec, Josef |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
15-25 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main result of this paper is Theorem 3.3: Every concrete logic (i.e., every set-representable orthomodular poset) can be enlarged to a concrete logic with a given automorphism group and with a given center. Since every sublogic of a concrete logic is concrete, too, and since not every state space of a (general) quantum logic is affinely homeomorphic to the state space of a concrete logic [8], our result seems in a sense the best possible. Further, we show that every group is an automorphism group of a concrete lattice logic and, on the other hand, we prove that this is not true for Boolean logics with a dense center. As a technical tool for pursuing the latter type of problems, we investigate the correspondence between homomorphisms of concrete logics and pointwise mappings of their domain. We prove that in a suitable topological representation of concrete logics, every automorphism is carried by a homeomorphism. (English) |
| Keyword:
|
orthomodular lattice |
| Keyword:
|
quantum logic |
| Keyword:
|
concrete logic |
| Keyword:
|
set representation |
| Keyword:
|
automorphism group of a logic |
| Keyword:
|
state space |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| MSC:
|
81C10 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 0742.06008 |
| idMR:
|
MR1118285 |
| . |
| Date available:
|
2008-10-09T13:10:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116938 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Navara M.: The independence of automorphism groups, centres and state spaces in quantum logics.to appear. |
| Reference:
|
[8] Navara M.: An alternative proof of Shultz's theorem.to appear. |
| Reference:
|
[9] Navara M., Pták P.: Almost Boolean orthomodular posets.J. Pure Appl. Algebra 60 (1989), 105-111. MR 1014608 |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
