Type-Decomposition of an Effect Algebra

Foundations of Physics 40 (9-10):1543-1565 (2010)
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Abstract

Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice

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Citations of this work

Type-Decomposition of a Synaptic Algebra.David J. Foulis & Sylvia Pulmannová - 2013 - Foundations of Physics 43 (8):948-968.

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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.
The Interpretation of Quantum Mechanics and the Measurement Process.Peter Mittelstaedt - 1998 - British Journal for the Philosophy of Science 49 (4):649-651.
Boolean Algebras.Roman Sikorski - 1966 - Journal of Symbolic Logic 31 (2):251-253.

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