Atomic Effect Algebras with the Riesz Decomposition Property

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Foundations of Physics 42 (8):1078-1093 (2012)
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Abstract

We discuss the relationships between effect algebras with the Riesz Decomposition Property and partially ordered groups with interpolation. We show that any σ-orthocomplete atomic effect algebra with the Riesz Decomposition Property is an MV-effect algebras, and we apply this result for pseudo-effect algebras and for states.

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10.1007/s10701-012-9655-7

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Citations of this work

Kite Pseudo Effect Algebras.Anatolij Dvurečenskij - 2013 - Foundations of Physics 43 (11):1314-1338.

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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.

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