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Foundations of Physics

, Volume 30, Issue 10, pp 1687–1706 | Cite as

MV and Heyting Effect Algebras

  • D. J. Foulis
Article

Abstract

We review the fact that an MV-algebra is the same thing as a lattice-ordered effect algebra in which disjoint elements are orthogonal. An HMV-algebra is an MV-effect algebra that is also a Heyting algebra and in which the Heyting center and the effect-algebra center coincide. We show that every effect algebra with the generalized comparability property is an HMV-algebra. We prove that, for an MV-effect algebra E, the following conditions are mutually equivalent: (i) E is HMV, (ii) E has a center valued pseudocomplementation, (iii) E admits a central cover mapping γ such that, for all p, q∈E, p∧q=0⇒γ(p)∧q=0.

Keywords

Cover Mapping Effect Algebra Generalize Comparability Comparability Property Heyting Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • D. J. Foulis
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of Massachusetts AmherstAmherst

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