Convergence in perfect MV-algebras
MV-algebras are the Lindenbaum algebras of the infinite-valued calculus of Łukasiewicz. In an earlier paper the authors investigated general order-convergence properties in MV-algebras, using the categorical equivalence \(\Gamma\) between MV-algebras and abelian lattice-ordered groups with strong unit [see \textit{D. Mundici}, ``Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus'', J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)]. In the present paper the authors focus their attention on the subclass of perfect MV-algebras. After defining the appropriate notion of Cauchy completion, they establish its existence and uniqueness.
scientific article; zbMATH DE number 1246339
scientific article