Isolation from Side in 2-Computably Enumerable Degrees

Abstract

In this work we consider isolation from side in different degree structures, in particular, in the 2-computably enumerable wtt-degrees and in low Turing degrees. Intuitively, a 2-computably enumerable degree is isolated from side if all computably enumerable degrees from its lower cone are bounded from above by some computably enumerable degree which is incomparable with the given one. It is proved that any properly 2-computably enumerable wtt-degree is isolated from side by some computable enumerable wtt-degree. Also it is shown that the same result holds for the low 2-computable enumerable Turing degrees.