ON REALIZATION OF EFFECT ALGEBRAS

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Authors

NIEDERLE Josef PASEKA Jan

Year of publication 2016
Type Article in Periodical
Magazine / Source Mathematica Slovaca
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1515/ms-2015-0140
Field General mathematics
Keywords non-classical logics; orthomodular lattices; effect algebras; MV-algebras; states; simplex algorithm
Description A well known fact is that there is a finite orthomodular lattice with an order determining set of states which is not order embeddable into the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a finite generalized effect algebra is order embeddable into the standard effect algebra E(H) of effects of a separable complex Hilbert space iff it has an order determining set of generalized states iff it is order embeddable into the power of a finite MV-chain. As an application we obtain an algorithm, which is based on the simplex algorithm, deciding whether such an order embedding exists and, if the answer is positive, constructing it. (C) 2016 Mathematical Institute Slovak Academy of Sciences
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