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Sharp and fuzzy elements of an RC-group

In: Mathematica Slovaca, vol. 56, no. 5
David Foulis
Detaily:
Rok, strany: 2006, 525 - 541
O článku:
Effect algebras serve as algebraic models for logical calculi and thereby provide semantic interpretations for both sharp and fuzzy logical propositions. Most of the effect algebras that are so employed can be realized as intervals in partially ordered abelian groups, called CB-groups, that are enriched by a family of order-preserving endomorphisms called compressions. For a special class of CB-groups called RC-groups, we show that every element of the positive cone can be decomposed uniquely as a sum of a finite chain of sharp elements and a fuzzy element of the unit interval that dominates no nonzero sharp element. The category of RC-groups includes the additive groups of bounded measurable functions on $σ$-fields of sets, abelian $\ell$-groups with Heyting MV-algebras as their unit intervals, and the self-adjoint parts of $AW*$-algebras.
Ako citovať:
ISO 690:
Foulis, D. 2006. Sharp and fuzzy elements of an RC-group. In Mathematica Slovaca, vol. 56, no.5, pp. 525-541. 0139-9918.

APA:
Foulis, D. (2006). Sharp and fuzzy elements of an RC-group. Mathematica Slovaca, 56(5), 525-541. 0139-9918.