Preprint Article Version 1 NOT YET PEER-REVIEWED

On the Independence of Effect Algebras’ Axioms

  1. Department of Mathematics, Faculty of Science, Ege University, 35100 ˙Izmir, Turkey
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 (doi: 10.20944/preprints201608.0208.v1). Senturk, I.; Oner, T. On the Independence of Effect Algebras’ Axioms. Preprints 2016, 2016080208 (doi: 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.

Subject Areas

quantum structures; effect algebras; fuzzy sets; independence

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