 One of Gödel’s goals was thus to provide a mathematical definition of the term “recursive” which generalizes prior examples of recursive definability in a manner but also captures to as great an extent as possible the class of functions computable by a finite procedure. This led him to define the so-called general recursive functions (see  Section 1.5)  whose isolation in turn played an important role in the formulation of Church’s Thesis (see  Section 1.6).  However Gödel’s definition also took place against the backdrop of other work which had been inspired by Hilbert’s original consideration of different forms of recursive definitions. It will now be useful to examine these developments.