Gudder, Stanley \(S\)-dominating effect algebras. (English) Zbl 0932.03072 Int. J. Theor. Phys. 37, No. 3, 915-923 (1998). 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. Cited in 1 ReviewCited in 19 Documents MSC: 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06C15 Complemented lattices, orthocomplemented lattices and posets Keywords:\(D\)-posets; \(S\)-dominating effect algebra; Brouwer-complementation; Brouwer-Zadeh poset; sharp elements; orthomodular lattice; Hilbert space effect algebra PDF BibTeX XML Cite \textit{S. Gudder}, Int. J. Theor. Phys. 37, No. 3, 915--923 (1998; Zbl 0932.03072) Full Text: DOI