BOTUR, Michal and Jan PASEKA. Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem. Algebra Universalis. BASEL: Birkhäuser Verlag, 2015, vol. 73, 3-4, p. 277-290. ISSN 0002-5240. Available from: https://dx.doi.org/10.1007/s00012-015-0329-0.
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Basic information
Original name Another proof of the completeness of the Lukasiewicz axioms and of the extensions of Di Nola's Theorem
Authors BOTUR, Michal (203 Czech Republic) and Jan PASEKA (203 Czech Republic, guarantor, belonging to the institution).
Edition Algebra Universalis, BASEL, Birkhäuser Verlag, 2015, 0002-5240.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
Impact factor Impact factor: 0.344
RIV identification code RIV/00216224:14310/15:00085224
Organization unit Faculty of Science
Doi http://dx.doi.org/10.1007/s00012-015-0329-0
UT WoS 000355208500005
Keywords in English MV-algebra; ultraproduct; Di Nola's Representation Theorem; Farkas' Lemma
Tags AKR, rivok
Changed by Changed by: prof. RNDr. Jan Paseka, CSc., učo 1197. Changed: 29/1/2016 23:35.
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 . 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.
Links
EE2.3.20.0051, research and development projectName: Algebraické metody v kvantové logice
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