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Representable effect algebras and observables. (English) Zbl 1308.81011
Summary: We introduce a class of monotone \(\sigma\)-complete effect algebras, called representable, which are \(\sigma\)-homomorphic images of a class of monotone \(\sigma\)-complete effect algebras of functions taking values in the interval \([0,1]\) and with effect algebra operations defined by points. We exhibit different types of compatibilities and show their connection to representability. Finally, we study observables and show situations when information of an observable on all intervals of the form \((-\infty,t)\) gives full information about the observable.

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