摘要

We survey the theory of Mucnik (weak) and Medvedev (strong) degrees of subsets of (omega)omega with particular attention to the degrees of Pi(0)(1) subsets of (omega)2. 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.