μMV-algebras: An approach to fixed points in Łukasiewicz logic

We study an expansion of MV-algebras, called μMV-algebras, in which minimal and maximal fixed points are definable. The first result is that μMV-algebras are termwise equivalent to divisible MVΔ-algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras and MVΔ-algebras. Using methods from the two known extensions we derive a number of results about μMV-algebras; among others: subdirect representation, standard completeness, amalgamation property and a description of the free algebra.