On the Upper Cone of Degrees Containing Hypersimple T-Mitotic Sets Which are not wtt-Mitotic

Abstract

Let us adduce some definitions. If A is a nonrecursive computably enumerable (c.e.) set, then a splitting of A is a pair A1, A2 of disjoint c.e. sets such that A1 U A2 = A.A c.e. set A is T-mitotic (wtt-mitotic) if there is a splitting A1, A2 of A such that A1 ≡T A2≡T A (A1 ≡wtt A2≡wtt A).In this article it is proved, that there exists a low c.e. degree u such that if v is a c.e. degree and u ≤ v, then v contains a hypersimple T-mitotic set, which is not wtt-mitotic.