Splitting of c.e. degrees and superlowness

Аннотация

In this paper, we show that for any superlow c.e. degrees $\dg a$ and $\dg b$ there exists a superlow c.e. degree $\dg c$ such that $\dg c\not=\dg a_0\cup\dg b_0$ for all c.e. degrees $\dg a_0\leqslant\dg a$, $\dg b_0\leqslant\dg b$.
This provides one more elementary difference between the classes of low c.e. degrees and superlow c.e. degrees.
We also prove that there is a c.e. degree that is not the supremum of any two superlow not necessarily c.e. degrees degrees.