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. and n-c.e. e-degrees are distinct. It is proved also that the structures 〈2n, ≤, 〉 and 〈2n, ≤. P〉 are not elementary equivalent where P is the predicate P(a) = “a is a e-degree”.