Classifying the provably total functions of PA
We give a self-contained and streamlined version of the classification of the provably computable functions of PA. The emphasis is put on illuminating as well as seems possible the intrinsic computational character of the standard cut elimination process. The article is intended to be suitable for teaching purposes and just requires basic familiarity with PA and the ordinals below ε₀. (Familiarity with a cut elimination theorem for a Gentzen or Tait calculus is helpful but not presupposed).
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1146620058
Digital Object Identifier: doi:10.2178/bsl/1146620058
Mathematical Reviews number (MathSciNet): MR2223920
Zentralblatt MATH identifier: 1118.03053