Article
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On the Independence of Effect Algebras’ Axioms
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Version 1
: Received: 25 August 2016 / Approved: 26 August 2016 / Online: 26 August 2016 (11:18:02 CEST)
How to cite: Senturk, I.; Oner, T. On the Independence of Effect Algebras’ Axioms. Preprints 2016, 2016080208. https://doi.org/10.20944/preprints201608.0208.v1 Senturk, I.; Oner, T. On the Independence of Effect Algebras’ Axioms. Preprints 2016, 2016080208. https://doi.org/10.20944/preprints201608.0208.v1
Abstract
In this paper, we scrutinize the axiomatic system of effect algebras which is given by D. J. Foulis and M.K. Bennett in the paper Effect Algebras and Unsharp Quantum Logics. We prove that this axiomatic system consists of independent axioms. To do this, we construct some models to indicate the indepence of each axiom. Therefore none of these axioms can be reduced when constructing any effect algebra. As a result, any algebra is an effect algebra if and only if it verifies (E1)-(E4) axioms.
Keywords
quantum structures; effect algebras; fuzzy sets; independence
Subject
Computer Science and Mathematics, Logic
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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