Isolation and the jump operator (Q2765575)

The paper deals with the Turing degrees of differences of recursively (= computably) enumerable degrees. The author constructs recursively enumerable sets \(A,B,C\) such that \(A\) has low\(_2\) Turing degree, the d.r.e.\ set \(D = B-C\) has high Turing degree and the Turing degree of \(D\) is isolated above \(A\), that is, every recursively enumerable set \(E\) below \(D\) is already below \(A\): \(E \leq_T D \Rightarrow E \leq_T A\). The author announces that the result can be improved: Together with Ishmukhametov he constructed \(A,B,C\) as above with the improvement that the Turing degree of \(A\) is low and not only low\(_2\).