Towards understanding the Pierce–Birkhoff conjecture via MV-algebras

S. Lapenta, I. Leuştean
2015 Fuzzy sets and systems (Print)  
Our main issue was to understand the connection between Ł 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 fMV-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
more » ... logical system can be seen as a local version of the Pierce-Birkhoff conjecture.
doi:10.1016/j.fss.2014.11.012 fatcat:blngfmis5rhvfnh3pj3j67gtdi