A Classification of Aperiodic Power Monoids Original Research Article

A picture is given of the poset of pseudovarieties generated by the power monoids of the members of given pseudovarieties of aperiodic monoids. It provides answers to various questions concerning power pseudovarieties, showing, in particular, that their classifying poset is a countably infinite lattice. Several related pseudovarieties are shown to have decidable membership problems.