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

Let us adduce some definitions. If A is a nonrecursive computably enumerable (c.e.) set, then a splitting of A is a pair A
₁
, A
₂
of disjoint c.e. sets such that A
₁
U A
₂
= A. A c.e. set A is T-mitotic (wtt-mitotic) if there is a splitting A
₁
, A
₂
of A such that A
₁
≡
_T
A
₂
≡
_T
A (A
₁
≡
_wtt
A
₂
≡
_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.