A survey of Mučnik and Medvedev degrees

Abstract

We survey the theory of Mučnik (weak) and Medvedev (strong) degrees of subsets of ^ωω with particular attention to the degrees of Π⁰₁ subsets of ^ω2. Sections 1—6 present the major definitions and results in a uniform notation. Sections 7—16 present proofs, some more complete than others, of the major results of the subject together with much of the required background material.