Isolated from above \(d\)-r. e. degrees. I (Q1293601)

A set \(A\subseteq\omega\) is said to be \(d\)-recursively enumerable (\(d\)-r.e.) if there exist recursively enumerable (r.e.) sets \(A_1\) and \(A_2\) such that \(A= A_1- A_2\). A Turing degree is called a \(d\)-r.e. degree if it contains a \(d\)-r.e. set; a \(d\)-r.e. degree is said to be properly \(d\)-r.e. if it is not an r.e. degree (does not contain r.e. sets). In the present article we study interaction between r.e. and \(d\)-r.e. degrees.