An Exercise in Programming in PA: Fast Growing Hierarchy Functions

Abstract

this paper is to illustrate that the techniques of computer programming can be used in mathematical logic. We apply the well-known list processing techniques to the task of introducing into PA (i.e. programming) the functions F of the Fast Growing Hierarchy (see [LW70,Wa70,Wa72,Ro84]). Although computationally unfeasible (already F! grows as Ackermann), the functions are important because all 0 -ordinal recursive functions, which are the provably recursive functions of PA, can be de ned from them by propositional connectives and bounded quanti cation, i.e. by 0 (fF j 0 g) formula