Precomplete Numberings

Abstract

In this survey, we discuss the theory of precomplete numberings, which appear frequently in computability theory. Precomplete numberings are closely related to some versions of the fixed-point theorem having an important methodological value. Sometimes, this allows one to replace cumbersome proofs based on the so-called priority method by elegant and simple applications of this theorem. In a sense, this paper covers the part of computability theory that may be developed by elementary methods.