Ackermann’s substitution method (remixed)

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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.

Keywords

Epsilon substitution method
Provably recursive functions

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Work partially supported by Marie Curie grant no. HPMF-CT-2002-015777.