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Orthogonal sets in effect algebras. (English) Zbl 0989.03071
A system of (not necessarily different) elements of an effect algebra is called \(\oplus\)-orthogonal if the sum of every finite subsystem exists. The author studies \(\oplus\)-orthogonal systems and shows, e.g., that a separable effect algebra is complete iff it is \(\sigma\)-complete, that a lattice effect algebra is complete iff every of its blocks is complete, and that every element of an Archimedean atomic lattice effect algebra is a sum of a \(\oplus\)-orthogonal system of atoms.

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