4 research outputs found
Homogeneous orthocomplete effect algebras are covered by MV-algebras
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
Representable Effect Algebras and Observables
We introduce a class of monotone -complete effect algebras, called
representable, which are -homomorphic images of a class of monotone
-complete effect algebras of functions taking values in the interval
and with pointwise defined effect algebra operations. We exhibit
different types of compatibilities and show their connection to
representability. Finally, we study observables and show situations when
information of an observable on all intervals of the form gives
full information about the observable
Triple Representation Theorem for orthocomplete homogeneous effect algebras
The aim of our paper is twofold. First, we thoroughly study the set of meager
elements , the set of sharp elements and the center in the
setting of meager-orthocomplete homogeneous effect algebras . Second, we
prove the Triple Representation Theorem for sharply dominating
meager-orthocomplete homogeneous effect algebras, in particular orthocomplete
homogeneous effect algebras.Comment: arXiv admin note: text overlap with arXiv:1203.6042 and
arXiv:1101.258
Galois connections and tense operators on q-effect algebras
For effect algebras, the so-called tense operators were already introduced by
Chajda and Paseka. They presented also a canonical construction of them using
the notion of a time frame.
Tense operators express the quantifiers "it is always going to be the case
that" and "it has always been the case that" and hence enable us to express the
dimension of time both in the logic of quantum mechanics and in the many-valued
logic.
A crucial problem concerning tense operators is their representation. Having
an effect algebra with tense operators, we can ask if there exists a time frame
such that each of these operators can be obtained by the canonical
construction. To approximate physical real systems as best as possible, we
introduce the notion of a q-effect algebra and we solve this problem for
q-tense operators on q-representable q-Jauch-Piron q-effect algebras.Comment: 14 page