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
Wilfried Buchholz (1995). Proof-Theoretic Analysis of Termination Proofs. Annals of Pure and Applied Logic 75 (1-2):57-65.
Toshiyasu Arai (1991). A Slow Growing Analogue to Buchholz' Proof. Annals of Pure and Applied Logic 54 (2):101-120.
Richard Sommer (1995). Transfinite Induction Within Peano Arithmetic. Annals of Pure and Applied Logic 76 (3):231-289.

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