Minimal generalized computable enumerations and high degrees

Abstract

© 2017, Pleiades Publishing, Ltd. We establish that the set of minimal generalized computable enumerations of every infinite family computable with respect to a high oracle is effectively infinite. We find some sufficient condition for enumerations of the infinite families computable with respect to high oracles under which there exist minimal generalized computable enumerations that are irreducible to the enumerations.