Comparing the degrees of enumerability and the closed Medvedev degrees

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees

On some filters and ideals of the Medvedev lattice

Let M be the Medvedev lattice: this paper investigates some filters and ideals (most of them already introduced by Dyment). If X is any of the filters or ideals considered, the questions concerning which we try to answer are: (1) is X prime? What is the cardinality of M/X ? Occasionally, we point out some general facts on the T-degrees or the partial degrees, by which these questions can be answered