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The Universal Group of a Heyting Effect Algebra

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Abstract

A Heyting effect algebra (HEA) is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties.

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Authors and Affiliations

  1. Emeritus Professor of Mathematics, University of Massachusetts, 1 Sutton Court, Amherst, MA, 01002, USA

    David J. Foulis

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  1. David J. Foulis
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Correspondence to David J. Foulis.

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Foulis, D.J. The Universal Group of a Heyting Effect Algebra. Stud Logica 84, 407–424 (2006). https://doi.org/10.1007/s11225-006-9015-8

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  • DOI: https://doi.org/10.1007/s11225-006-9015-8

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