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On three notions of orthosummability in orthoalgebras. (English) Zbl 0957.03061
Summary: We consider three notions of orthosummability for orthoalgebras that were recently introduced by Habil, Wilce, and Younce, respectively. Habil’s orthosummability is shown to be equivalent to Wilce’s. Younce’s orthosummability is shown to be equivalent to Habil/Wilce’s under the assumption that all blocks are suborthosummable.

MSC:
03G12 Quantum logic
06C15 Complemented lattices, orthocomplemented lattices and posets
46L51 Noncommutative measure and integration
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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