On the existence of the tt-mitotic hypersimple set which is not btt-mitotic

摘要

Let us adduce some definitions: If a recursively enumerable (r.e.) set A is a disjoint union of two sets B and C, then we say that B, C is an r.e. splitting of A The r.e. set A is tt-mitotic (btt-mitotic) if there is an r.e. splitting (B, C) of A such that the sets B and C both belong to the same tt - (btt -) degree of unsolvability, as the set A. In this paper the existence of the tt-mitotic hypersimple set, which is not btt-mitotic is proved.