Some Properties of the Upper Semilattice of Computable Families of Computably Enumerable Sets

Abstract

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 the question whether there exist atoms and coatoms in the factor semilattice of Ω with respect to an ideal of finite families. Also we point out a sufficient condition for computable families to be complemented.