MV and Heyting Effect Algebras

Foundations of Physics 30 (10):1687-1706 (2000)
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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

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References found in this work

The theory of Representations for Boolean Algebras.M. H. Stone - 1936 - Journal of Symbolic Logic 1 (3):118-119.
Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Paraconsistent quantum logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.
Lattice Theory.Garrett Birkhoff - 1950 - Journal of Symbolic Logic 15 (1):59-60.

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