Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 63, Issue 3 (1998), 897-925.
Variations on a Theme by Weiermann
Weiermann  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 $\theta\alpha$n is described as follows. For each ordinal $\alpha$ and natural number n let T$^\alpha_n$ 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$^\alpha_n$ is well founded and hence finite by Konig's lemma. Define $\theta\alpha$n=the depth of the tree T$^\alpha_n$=the length of the longest branch in T$^\alpha_n$. 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.
J. Symbolic Logic, Volume 63, Issue 3 (1998), 897-925.
First available in Project Euclid: 6 July 2007
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Arai, Toshiyasu. Variations on a Theme by Weiermann. J. Symbolic Logic 63 (1998), no. 3, 897--925. https://projecteuclid.org/euclid.jsl/1183745573