Non-isolated quasi-degrees

摘要

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.