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\(S\)-dominating effect algebras. (English) Zbl 0932.03072
Summary: A special type of effect algebra called an \(S\)-dominating effect algebra is introduced. It is shown that an \(S\)-dominating effect algebra \(P\) has a naturally defined Brouwer-complementation that gives \(P\) the structure of a Brouwer-Zadeh poset. This enables us to prove that the sharp elements of \(P\) form an orthomodular lattice. We then show that a standard Hilbert space effect algebra is \(S\)-dominating. We conclude that \(S\)-dominating effect algebras may be useful abstract models for sets of quantum effects in physical systems.

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