On some filters and ideals of the Medvedev lattice

Let \(\mathfrak{M}\) be the Medvedev lattice: this paper investigates some filters and ideals (most of them already introduced by Dyment, 4]) of \(\mathfrak{M}\) . If \(\mathfrak{G}\) is any of the filters or ideals considered, the questions concerning \(\mathfrak{G}\) which we try to answer are: (1) is \(\mathfrak{G}\) prime? What is the cardinality of \({\mathfrak{M} \mathord{\left/ {\vphantom {\mathfrak{M} \mathfrak{G}}} \right. \kern-0em} \mathfrak{G}}\) ? Occasionally, we point out some general facts on theT-degrees or the partial degrees, by which these questions can be answered.