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arXiv · 1410.5593

Towards understanding the Pierce-Birkhoff conjecture via MV-algebras

Serafina Lapenta·Ioana Leustean
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Abstract

Our main issue was to understand the connection between Łukasiewicz 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 $[0,1]$. The proper quasi-variety generated by $[0,1]$, 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.

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BibTeXRIS

Serafina Lapenta, Ioana Leustean. 2014-11-13. Towards understanding the Pierce-Birkhoff conjecture via MV-algebras. https://doi.org/10.1016/j.fss.2014.11.012

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