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Effect algebras and para-Boolean manifolds. (English) Zbl 0985.81009

Summary: It is shown that every effect algebra can be represented as a pasting of a system where each element is the range of an unsharp observable. To describe the range of an unsharp observable algebraically, the notion of a “para-Boolean quasi-effect algebra” is introduced. Some intrinsic compatibility conditions ensuring commensurability of effects are studied.

MSC:

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