On generating and concreteness in quantum logics. (English) Zbl 0771.03023
It is known that there are infinite orthomodular lattices which are finitely generated. As an analogue, the author presents a (quite nontrivial) example of an infinite logic (= orthomodular poset) with finitely many generators (it is generated using the orthocomplementation and orthogonal joins, without the use of other lattice operations). This logic is necessarily non-concrete (it does not admit a set representation), but all its finite sublogics are concrete.
Reviewer: M.Navara (Praha)
MSC:
| 03G12 | Quantum logic |
| 81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
| 06C15 | Complemented lattices, orthocomplemented lattices and posets |
References:
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| [3] | GUDDER S. P.: Stochastic Methods in Quantum Mechanics. North Holland, New York, 1979. · Zbl 0439.46047 |
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