muMV-algebras: an approach to fixed points in Lukasiewicz logic

We study an expansion of MV-algebras, called $\mu$MV-algebras, in which minimum and maximum fixed points are definable. The first result is that $\mu$MV-algebras are term-wise equivalent to divisible MV$_\Delta$ algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras and MV$_\Delta$ algebras. Using methods from the two known extensions we derive a number of results about $\mu$MV-algebras; among others: subdirect representation, standard completeness, amalgamation property and a description of the free algebra.

muMV-algebras: an approach to fixed points in Lukasiewicz logic