Sharp and Meager Elements in Orthocomplete Homogeneous Effect Algebras

Homogeneous orthocomplete effect algebras are covered by MV-algebras

Generalized homogeneous, prelattice and MV-effect algebras

We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra P are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We pr...

Effect algebras with the maximality property

The maximality property was introduced in [9] in orthomodular posets as a common generalization of orthomodular lattices and orthocomplete orthomodular posets. We show that various conditions used in the theory of effect algebras are stronger than the maximality property, clear up the connections between them and show some consequences of these conditions. In particular, we prove that a Jauch–P...

Basic decomposition of elements and Jauch-Piron effect algebras

A logical structure of propositions associated with a physical system,which can be xperimentally tested,form in the clasical case a Boolean algebra and in a quantum mechanical case an orthomodular lattice or poset (a quantum logic). Recently new logical structures for the presence of propositions, properties,questions or events with fuzziness,uncertainity or unsharpness has been introduced: Eff...

Central Elements, Blocks and Sharp Elements of Lattice Effect Algebras

For every central element z of a lattice effect algebra E, the interval [0, z] with the ⊕ operation inherited from E and the new unity z is a lattice effect algebra in its own right. We show connections between blocks, sharp elements and central elements of [0, z] and those of E. We prove that except for central elements, the intervals [0, z] are closed with respect to the ⊕-operation also for ...