© 2020, Springer Science+Business Media, LLC, part of Springer Nature. We point out an existence criterion for positive computable total Π11 -numberings of families of subsets of a given Π11 -set. In particular, it is ...

We look at specific features of the algebraic structure of an upper semilattice of computable families of computably enumerable sets in Ω. It is proved that ideals of minuend and finite families of Ω coincide. We deal with ...