On some filters and ideals of the Medvedev lattice

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${\mathfrak{M} \mathord{\left/ {\vphantom {\mathfrak{M} \mathfrak{G}}} \right. \kern-\nulldelimiterspace} \mathfrak{G}}$? Occasionally, we point out some general facts on theT-degrees or the partial degrees, by which these questions can be answered.