Non-isolated quasi-degrees

Abstract

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 also prove that below any c.e. Q-degree there is a 2-c.e. Q-degree, which is non-isolated from below and from above. © 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.