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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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