Convergence with a fixed regulator in perfect MV-algebras

MV-algebras were introduced by Chang as an algebraic counterpart of the Łukasiewicz infinite-valued logie. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investigate the convergence with a fixed regulator in perfect MV-algebras using Di Nola-Lettieri functors. The main result of the paper states that every locally Archimedean MV-algebra has a unique v-Cauchy completion.