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David J. Foulis 《Studia Logica》2006,84(3):407-424
A Heyting effect algebra (HEA) is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides
with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval
in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its
universal group has the central comparability and central Rickart properties.
Presented by Daniele Mundici 相似文献
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We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries. 相似文献
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Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state. 相似文献
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