Journal of Symbolic Logic

Variations on a Theme by Weiermann

Toshiyasu Arai

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Abstract

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 $\theta\alpha$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.

Article information

Source
J. Symbolic Logic, Volume 63, Issue 3 (1998), 897-925.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745573

Mathematical Reviews number (MathSciNet)
MR1649068

Zentralblatt MATH identifier
0919.03043

JSTOR
links.jstor.org

Citation

Arai, Toshiyasu. Variations on a Theme by Weiermann. J. Symbolic Logic 63 (1998), no. 3, 897--925. https://projecteuclid.org/euclid.jsl/1183745573


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