Homogeneous orthocomplete effect algebras are covered by MV-algebras

Details Homogeneous orthocomplete effect algebras are covered by MV-algebras Homogeneous orthocomplete effect algebras are covered by MV-algebras

2012-03-27

arxiv.org/abs/1203.6042v1

Mathematics

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Scientific paper

The aim of our paper is twofold. First, we thoroughly study the set of meager elements Mea(E) and the set of hypermeager elements HMea(E) in the setting of homogeneous effect algebras E. Second, we study the property (W+) and the maximality property introduced by Tkadlec as common generalizations of orthocomplete and lattice effect algebras. We show that every block of an Archimedean homogeneous effect algebra satisfying the property (W+) is lattice ordered. Hence such effect algebras can be covered by ranges of observables. As a corollary, this yields that every block of a homogeneous orthocomplete effect algebra is lattice ordered. Therefore finite homogeneous effect algebras are covered by MV-algebras.

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