zbMATH — the first resource for mathematics

Boolean embeddings and hidden variables. (English) Zbl 0641.03041
In this rather disjointed paper the author first examines two existing methods of embedding orthomodular posets into a Boolean algebra, working through the proofs of Marlow and Zierler and Schlessinger claiming minor simplifications.
In the last (and much the shortest) section, the author then attempts to relate the discussion of embeddings to hidden variables. In contrast to the earlier proofs this section is very sketchy. Briefly a system is an ordered pair (L,S) where L is an orthomodular poset and S a set of “realisable states”, which are functions from L to \(<0,1>\). The author takes the issue of hidden variables to be a question of whether any system (L,S) can be extended to a system \(<B,S>\), where B is now a Boolean algebra and the states are extensions of the states on L.
The concepts are not developed here, or even properly defined, although the author does work through some examples of systems which can and cannot be extended in this way to Boolean systems.
Reviewer: R.Wallace Garden
03G12 Quantum logic
06A06 Partial orders, general
PDF BibTeX Cite
Full Text: EuDML