#### Title:

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

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#### Uncontrolled Keywords:

wtt-mitotic ; hypersimple T-mitotic sets ; nonrecursive computably enumerable set

#### Abstract:

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.

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#### DOI:

10.1109/CSITechnol.2019.8895074

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#### Affiliation:

Institute for Informatics and Automation Problems of NAS RA

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#### Conference title:

2019 Computer Science and Information Technologies (CSIT)