There are no maximal low d.c.e. degrees (Q558429)

The main result of the paper is Theorem 1.6 showing that there is no maximal low d.c.e. degree. Besides, a number of different results concerning d.c.e.degrees are discussed. We recall that a set \(A\) is d.c.e. if \(A\) is a difference of two computably enumerable sets. Turing d.c.e. degrees, i.e. degrees containing d.c.e sets, were studied more or less intensively during the last 10--15 years when a number of significant results concerning d.c.e. degrees have been obtained including the famous `Non-Density Theorem' by Cooper, Harrington, Lachlan, Lempp and Soare. The paper is useful for all people interested in the modern development of computability theory.