Foundations of Physics

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

MV and Heyting Effect Algebras

  • D. J. Foulis


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.


Cover Mapping Effect Algebra Generalize Comparability Comparability Property Heyting Algebra 
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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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