Abstract

We aim at a conceptually clear and technically smooth investigation of Ackermann’s substitution method [W. Ackermann, Zur Widerspruchsfreiheit der Zahlentheorie, Math. Ann. 117 (1940) 162–194]. Our analysis provides a direct classification of the provably recursive functions of PA(ε), i.e. Peano Arithmetic framed in the ε-calculus.

BibTeX

@article{GM-APAL06,
  author    = "Georg Moser",
  title     = "Ackermann's Substitution Method (remixed)",
  journal   = "Annals of Pure and Applied Logic",
  volume    = 142,
  number    = "1-3",
  year      = 2006,
  pages     = "1--18"
}