An elementary proof of the completeness of the Lukasiewicz axioms

4 pages•Published: July 28, 2014

Abstract

The main aim of this talk is twofold. Firstly, to present an elementary
method based on Farkas' lemma for rationals how to embed any finite partial subalgebra
of a linearly ordered MV-algebra into Q \ [0; 1] and then to establish a new elementary
proof of the completeness of the Lukasiewicz axioms for which the MV-algebras community
has been looking for a long time. Secondly, to present a direct proof of Di Nola's
representation Theorem for MV-algebras and to extend his results to the restriction of
the standard MV-algebra on rational numbers.

Keyphrases: di nolas representation theorem, farkas lemma, mv algebra, ultraproduct

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 35-38.

Links:	https://easychair.org/publications/paper/QDx
	https://doi.org/10.29007/s5h9

BibTeX entry

@inproceedings{TACL2013:elementary_proof_completeness_Lukasiewicz,
  author    = {Michal Botur and Jan Paseka},
  title     = {An elementary proof of the completeness of the Lukasiewicz axioms},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/QDx},
  doi       = {10.29007/s5h9},
  pages     = {35-38},
  year      = {2014}}

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