Abstract

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