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Compatibility and decompositions of effects. (English) Zbl 1059.81016
Summary: Compatibility relations in effect algebras and their connections with refinements of the orthogonal partitions of unity are studied. Properties of blocks as maximal sets of compatible elements are discussed. Some special kinds of effect algebras are characterized using properties of compatibility. Using refinements, an additional structure on the effect test spaces is introduced and used to a characterization of different types of effect algebras.

MSC:
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06C15 Complemented lattices, orthocomplemented lattices and posets
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