ABSTRACT
The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. This chapter contains several propositions for determining recursively enumerable relations. A relation is recursively enumerable (abbreviated RE) if it is the domain of a recursive function. It discusses the Church's Thesis, in which a relation is RE iff it is semicomputable. People can use implicit definitions to define RE relations. The chapter also presents the Selector Theorem, Graph Theorem, and Corollary.
