Lattice Embeddings into the R . E . Degrees Preserving 0 and 1 Klaus Ambos - Spies

Lattice Embeddings into the R . E . Degrees Preserving 0 and 1

We show that a nite distributive lattice can be embedded into the r.e. degrees preserving least and greatest element i the lattice contains a join-irreducible noncappable element.

2 Klaus Ambos - Spies , Steffen Lempp

We show that the two nondistributive ve-element lattices, M 5 and N 5 , can be embedded into the r.e. degrees preserving the greatest element.

Undecidability and 1-types in intervals of the computably enumerable degrees

The Continuity of Cupping to 0 0

It is shown that, if a, b are recursively enumerable degrees such that 0 < a < 0 0 and a b = 0 0 , then there exists a recursively enumerable degree c such that c < a and c b = 0 0 .

Generating Sets for the Recursively Enumerable Turing Degrees

One of the recurrent themes in the area of the recursively enumerable (r.e.) degrees has been the study of the meet operator. While, trivially, the partial ordering of the r.e. degrees is an upper semi-lattice, i.e., the join ∗Lempp was partially supported by NSF grant DMS-0140120 and a Mercator Guest Professorship of the Deutsche Forschungsgemeinschaft. †Slaman was partially supported by the A...