2014/11/18 by Lapenta, Serafina, Leustean, Ioana
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1411.4987
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras by adjunctions, using the tensor product of MV-algebras and defining the tensor PMV-algebra of a semisimple MV-algebra, inspired by the construction of the tensor algebra of a vector space. We further apply the main results to prove amalgamation properties and, via categorical equivalence, we transfer all results to the framework of lattice- ordered groups.