Embeddings into the Computably Enumerable Degrees

Extensions of Embeddings below Computably Enumerable Degrees

Toward establishing the decidability of the two quantifier theory of the ∆ 2 Turing degrees with join, we study extensions of embeddings of upper-semi-lattices into the initial segments of Turing degrees determined by computably enumerable sets, in particular the degree of the halting set 0. We obtain a good deal of sufficient and necessary conditions.

Extensions of Embeddings in the Computably Enumerable Degrees

Embedding the Diamond Lattice in the c.e. tt-Degrees with Superhigh Atoms

The notion of superhigh computably enumerable (c.e.) degrees was first introduced by Mohrherr in [7], where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in [4] that the diamond ...

A superhigh diamond in the c.e. tt-degrees

The notion of superhigh computably enumerable (c.e.) degrees was first introduced by Mohrherr in [7], where she proved the existence of incomplete superhigh c.e. degrees, and high, but not superhigh, c.e. degrees. Recent research shows that the notion of superhighness is closely related to algorithmic randomness and effective measure theory. Jockusch and Mohrherr proved in [4] that the diamond ...

Algebraic aspects of the computably enumerable degrees.

A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. The class of sets B which contain the same information as A under Turing computability (</=T) is the (Turing) degree of A, and a degree is c.e. if it contains a c.e. set. The extension of embedding problem for the c.e. degrees R = (R, ...