Splitting properties of n-C.E. enumeration degrees

It is proved that if 1 < m < 2p ≤ n for some integer p then the elementary theories of posets of m-c.e. n-c.e. e-degrees are distinct. It is proved also that the structures 〈D2n ≤ P〉 and 〈D2n ≤ P〉 are not elementary equivalent where P is the predicate P(a) = "a is a π1 0 e-degree"

Minimal bounds and members of effectively closed sets

We show that there exists a non-empty $\Pi^0_1$ class, with no recursive element, in which no member is a minimal cover for any Turing degree.Comment: 15 pages, 4 figures, 1 acknowledgemen