Towards understanding the Pierce-Birkhoff conjecture via MV-algebras
Logic
2016-05-05 v2
Abstract
Our main issue was to understand the connection between \L ukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of \textit{f}MV-algebras, which are MV-algebras endowed with both an internal binary product and a scalar product with scalars from . The proper quasi-variety generated by , with both products interpreted as the real product, provides the desired framework: the normal form theorem of its corresponding logical system can be seen as a local version of the Pierce-Birkhoff conjecture.
Keywords
Cite
@article{arxiv.1410.5593,
title = {Towards understanding the Pierce-Birkhoff conjecture via MV-algebras},
author = {Serafina Lapenta and Ioana Leustean},
journal= {arXiv preprint arXiv:1410.5593},
year = {2016}
}