The universal group of a Heyting effect algebra

Studia Logica 84 (3):407 - 424 (2006)
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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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References found in this work

Algebraic foundations of many-valued reasoning.Roberto Cignoli - 1999 - Boston: Kluwer Academic Publishers. Edited by Itala M. L. D'Ottaviano & Daniele Mundici.
Effect algebras and unsharp quantum logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
Phi-symmetric effect algebras.M. K. Bennett & D. J. Foulis - 1995 - Foundations of Physics 25 (12):1699-1722.
MV and Heyting Effect Algebras.D. J. Foulis - 2000 - Foundations of Physics 30 (10):1687-1706.

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