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Blocks in pairwise summable generalized effect algebras. (English) Zbl 1310.81018
Summary: We study the so-called pairwise summable generalized effect algebras and show some conditions under which they are generalized MV-effect algebras. Moreover, we give a necessary and sufficient condition for finite antichains of elements in pairwise summable generalized effect algebras under which they are sets of atoms of sub-generalized effect algebras, which are generalized MV-effect algebras in their own right. Simultaneously, we give counterexamples which show properties of those antichains which are not necessary or sufficient to be atoms of such generalized MV-effect algebras.
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
06A06 Partial orders, general
06C15 Complemented lattices, orthocomplemented lattices and posets
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