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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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