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A note on observables on MV-algebras. (English) Zbl 1005.06006
Summary: A criterion when a subset of an MV-algebra is contained in the range of a (finitely additive) observable is given. It is used to prove that every at most countable subset of any MV-algebra is contained in the range of an observable. A much stronger result holds for any bold fuzzy algebra \([0,1]^S\) which is wholly contained in the range of a (\(\sigma \)-additive) observable.

MSC:
06D35 MV-algebras
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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