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@article{1320849, author = {Botur, Michal and Paseka, Jan}, article_location = {BASEL}, article_number = {3-4}, doi = {http://dx.doi.org/10.1007/s00012-015-0329-0}, keywords = {MV-algebra; ultraproduct; Di Nola's Representation Theorem; Farkas' Lemma}, language = {eng}, issn = {0002-5240}, journal = {Algebra Universalis}, title = {Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem}, volume = {73}, year = {2015} }
TY - JOUR ID - 1320849 AU - Botur, Michal - Paseka, Jan PY - 2015 TI - Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem JF - Algebra Universalis VL - 73 IS - 3-4 SP - 277-290 EP - 277-290 PB - Birkhäuser Verlag SN - 00025240 KW - MV-algebra KW - ultraproduct KW - Di Nola's Representation Theorem KW - Farkas' Lemma N2 - 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. ER -
BOTUR, Michal a Jan PASEKA. Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem. \textit{Algebra Universalis}. BASEL: Birkhäuser Verlag, 2015, roč.~73, 3-4, s.~277-290. ISSN~0002-5240. Dostupné z: https://dx.doi.org/10.1007/s00012-015-0329-0.
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