We show that non-isolated from below 2-c.e. Q-degrees are dense in the structure of c.e. Q-degrees. We construct a 2-c.e. Q-degree, which can't be isolated from below not only by c.e. Q-degrees, but by any Q-degree. We ...
We prove a completeness criterion for quasi-reducibility and generalize it to higher levels of the arithmetical hierarchy. As an application of the criterion we obtain Q-completeness of the set of all pairs (x, n) such ...