Numerical representations of orthomodular lattices and Boolean algebras with infinite operations. (English) Zbl 0581.06007

Strojewski, Dariusz

Bull. Pol. Acad. Sci., Math. 33, 341-348 (1985).

M. J. Mączyński and T. Traczyk [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 21, 3-8 (1973; Zbl 0265.06003)] gave a necessary and sufficient condition for a set of functions to represent an orthomodular poset with an order-determining set of states. The author of the paper reviewed finds an alternative characterization. Then he obtains a characterization of orthomodular lattices and applies his results to lattices and Boolean algebras with infinite operations.

Reviewer: P.Ptak

MSC:

06C15	Complemented lattices, orthocomplemented lattices and posets
06E10	Chain conditions, complete algebras
81P10	Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)

Keywords:

orthomodular poset; order-determining set of states; orthomodular lattices; Boolean algebras with infinite operations

Citations:

Zbl 0265.06003