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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.

MSC:
 03G12 Quantum logic 06C15 Complemented lattices, orthocomplemented lattices and posets 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)