Variations on a theme by Weiermann

Journal of Symbolic Logic 63 (3):897-925 (1998)
Weiermann [18] introduces a new method to generate fast growing functions in order to get an elegant and perspicuous proof of a bounding theorem for provably total recursive functions in a formal theory, e.g., in PA. His fast growing function θαn is described as follows. For each ordinal α and natural number n let T α n denote a finitely branching, primitive recursive tree of ordinals, i.e., an ordinal as a label is attached to each node in the tree so that the labelling is compatible with the tree ordering. Then the tree T α n is well founded and hence finite by Konig's lemma. Define θαn=the depth of the tree T α n =the length of the longest branch in T α n . We introduce new fast and slow growing functions in this mode of definitions and show that each of these majorizes provably total recursive functions in PA
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DOI 10.2307/2586719
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References found in this work BETA
Elementary Descent Recursion and Proof Theory.Harvey Friedman & Michael Sheard - 1995 - Annals of Pure and Applied Logic 71 (1):1-45.
Proof-Theoretic Analysis of Termination Proofs.Wilfried Buchholz - 1995 - Annals of Pure and Applied Logic 75 (1-2):57-65.
Transfinite Induction Within Peano Arithmetic.Richard Sommer - 1995 - Annals of Pure and Applied Logic 76 (3):231-289.
A Slow Growing Analogue to Buchholz' Proof.Toshiyasu Arai - 1991 - Annals of Pure and Applied Logic 54 (2):101-120.

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2004 Summer Meeting of the Association for Symbolic Logic.Wolfram Pohlers - 2005 - Bulletin of Symbolic Logic 11 (2):249-312.

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