Abstract
The main aim of this paper is twofold. Firstly, to present a new method based on Farkas’ Lemma for the rational numbers, showing how to embed any finite partial subalgebra of a linearly ordered MV-algebra into \({\mathbb{Q}\cap[0, 1]}\). and then to establish a new proof of the completeness of the Łukasiewicz axioms based on this method. Secondly, to present a purely algebraic proof of Di Nola’s Representation Theorem for MV-algebras and to extend his results to the restriction of the standard MV-algebra on the rational numbers.
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Presented by S. Pulmannova.
Both authors gratefully acknowledge the support by ESF Project CZ.1.07/2.3.00/20.0051 Algebraic methods in Quantum Logic of the Masaryk University. M. Botur gratefully acknowledges Financial Support of the Grant Agency of the Czech Republic under the grant No. GAČR P201/11/P346.
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Botur, M., Paseka, J. Another proof of the completeness of the Łukasiewicz axioms and of the extensions of Di Nola’s Theorem. Algebra Univers. 73, 277–290 (2015). https://doi.org/10.1007/s00012-015-0329-0
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DOI: https://doi.org/10.1007/s00012-015-0329-0