Open AccessOn Initial Segments of Turing Degrees Containing Simple T-Mitotic but not wtt-Mitotic Sets
Author(s) -
Arsen H. Mokatsian
Publication year - 2019
Publication title -
mathematical problems of computer science
Language(s) - English
Resource type - Journals
eISSN - 2738-2788
pISSN - 2579-2784
DOI - 10.51408/1963-0039
Subject(s) - simple (philosophy) , mathematics , turing , set (abstract data type) , degree (music) , mitosis , combinatorics , recursively enumerable language , discrete mathematics , computer science , biology , physics , microbiology and biotechnology , philosophy , epistemology , acoustics , programming language
We consider the properties of computably enumerable (c.e.) Turing degrees containing sets, which possess the property of a T-mitotic splitting but don't have a wtt-mitotic splitting. It is proved that for any noncomputable c.e. degree b there exists a degree a, such that a · b and a contains a simple T- itotic set, which is not wtt-mitotic.