SOME RESULTS ON THE UPPER-SEMILATTICE OF R.E. $m$-DEGREES INSIDE A SINGLE R.E. $tt$-DEGREE

Abstract

In this paper it is shown that: 1) There exists such a tt-degree which contains infinitely many m-degrees of the type of $\omega^k$ for any positive natural number k; 2) There exists such a $tt$-degree which contains infinitely many m-degrees of the type of $\mathbb{Q}$ of rational numbers.