SOME EFFECTIVELY INFINITE CLASSES OF ENUMERATIONS

This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Roger's semilattice. We introduce a notion of effective infinity of classes of computable e numerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite f or classes of all enumerations without repetitions, positive undecidab le enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to streng then the results of Pour-El, Pour-El and Howard, Ershov and Khutoretsk ii about existence of enumerations without repetitions and positive un decidable enumerations.