Publication details
Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Algebra Universalis |
| MU Faculty or unit | |
| Citation | |
| Doi | https://doi.org/10.1007/s00012-015-0329-0 |
| Field | General mathematics |
| Keywords | MV-algebra; ultraproduct; Di Nola's Representation Theorem; Farkas' Lemma |
| Description | 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 . and then to establish a new proof of the completeness of the Lukasiewicz 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. |