Irreducible, Singular, and Contiguous Degrees

Abstract

We study structures of degrees of stronger algorithmic reducibilities inside the degrees of weaker algorithmic ones. Results in this area are reviewed for algorithmic reducibilities m-, 1-, tt-, wtt-, T-, e-, s-, Q-, and we formulate questions that are still not settled for these. A computably enumerable Q-degree which consists of one computably enumerable m-degree is constructed.