On very high degrees

Abstract

In this paper we show that there is a pair of superhigh r.e. degree that forms a minimal pair. An analysis of the proof shows that a critical ingredient is the growth rates of certain order functions. This leads us to investigate certain high r.e. degrees, which resemble ∅’ very closely in terms of ∅’-jump traceability. In particular, we will construct an ultrahigh degree which is cappable.