Recursively Enumerable Sets

Abstract

In this chapter we shall deal in some detail with the set Σ₁ of relations (see 5.24). Such relations are called recursively enumerable for reasons which will shortly become clear. The study of recursively enumerable relations is one of the main branches of recursive function theory. They play a large role in logic. In fact, for most theories the set of Gödel numbers of theorems is recursively enumerable. Thus many of the concepts introduced in this section will have applications in our discussion of decidable and undecidable theories in Part III. Unless otherwise stated, the functions in this chapter are unary.