MV and Heyting Effect Algebras |
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Authors: | D J Foulis |
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Institution: | (1) Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts, 01003 |
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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 such that, for all p, q E, p q=0![rArr](/content/x03kw7461060514v/xxlarge8658.gif) (p) q=0. |
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