Classifying the provably total functions of pa

Bulletin of Symbolic Logic 12 (2):177-190 (2006)
Abstract
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)
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Andreas Weiermann (2009). Phase Transitions for Gödel Incompleteness. Annals of Pure and Applied Logic 157 (2):281-296.
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