chapter  7
10 Pages

The Arithmetization of Syntax

The study of undefinability and incompleteness in Chapter 4 did depend on assumptions about functions g j , gp, gg which coded the objects of a lan­ guage L . I now shall show that these functions can be defined in many situ­ ations arising in mathematical practise, and I shall also show that such defi­ nitions then have the consequence that the sets, relations and functions, which correspond to these objects, become recursive, if not elementary - in particular the substitution function sub and the deduction relation ded.