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On the concreteness of quantum logics. (English) Zbl 0586.03050
The authors take the very conventional view of quantum logic as an orthomodular poset and conduct a very traditional enquiry into its relation to classical Boolean logic. That is, they attempt to find a natural relation between the structure of this orthomodular poset and the classical structure of a subset of sets. The meagreness of their results should serve to show that this traditional approach has proved unfruitful. The authors do not attempt to relate their discussion to quantum mechanics.
In fact the authors establish a relation between the ”centres”, i.e. the globally compatible elements, of the orthomodular posets and the centres of ”concrete” logics, i.e. of orthocomplemented posets with 1 and 0 which are isomorphic to a collection of subsets of a set. This result will probably be of interest only to the most devoted ”quantum logicians”. They also, perhaps more interestingly, establish an embedding of orthocomplemented posets into concrete logics.
Reviewer: R.Wallace Garden

MSC:
03G12 Quantum logic
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