Major sets, classes of simple sets, and Q-complete sets (Q1810051)

In this paper, the author shows that every nonrecursive r.e. (recursively enumerable) set has a Q-complete major set. An r.e. set \(A\) is called Q-complete if each r.e. set Q-reduces to \(A\), where a set \(B\) Q-reduces to \(A\) if there exists a general recursive function \(f\) such that \((\forall x)(x\in B \Longleftrightarrow W_{f(x)}\subseteq A)\). In addition, the author gives various classes of simple sets which contain Q-complete sets.