| Title:
|
On the concreteness of quantum logics (English) |
| Author:
|
Pták, Pavel |
| Author:
|
Wright, John D. Maitland |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
30 |
| Issue:
|
4 |
| Year:
|
1985 |
| Pages:
|
274-285 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that for any quantum logic $L$ one can find a concrete logic $K$ and a surjective homomorphism $f$ from $K$ onto $L$ such that $f$ maps the centre of $K$ onto the centre of $L$. Moreover, one can ensure that each finite set of compatible elements in $L$ is the image of a compatible subset of $K$. This result is "best possible" - let a logic $L$ be the homomorphic image of a concrete logic under a homomorphism such that, if $F$ is a finite subset of the pre-image of a compatible subset of $L$, then $F$ is compatible. Then $L$ must be concrete. In the second part one considers embeddings into concrete logics. It is shown that any concrete logic can be embedded into a concrete logic with preassigned centre and an abundance of two-valued measures. Finally, one proves that an arbitrary logic can be mapped into a concrete logic by a centrally additive mapping which preserves the ordering and complementation. (English) |
| Keyword:
|
orthomodular lattice |
| Keyword:
|
orthomodular poset |
| Keyword:
|
centres |
| Keyword:
|
orthocomplemented posets |
| Keyword:
|
concrete logics |
| MSC:
|
03G12 |
| MSC:
|
06C15 |
| MSC:
|
81B10 |
| idZBL:
|
Zbl 0586.03050 |
| idMR:
|
MR0795987 |
| DOI:
|
10.21136/AM.1985.104150 |
| . |
| Date available:
|
2008-05-20T18:27:46Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104150 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] R. Godowski: Varieties of orthomodular lattices with a strongly full set of states.Demonstration Mathematica, Vol. XIV, No. 3, (1981). Zbl 0483.06007, MR 0663122 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] S. Pulmannová: Compatibility and partial compatibility in quantum logics.Ann. Inst. Henri Poincaré, Vol. XXXIV, No. 4, 391-403 (1981). MR 0625170 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
