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Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games

In: Gentzen's Centenary

Author

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  • Frederik Meskens

    (Gent Universitet, Vakgroep Wiskunde)

  • Andreas Weiermann

    (Gent Universitet, Vakgroep Wiskunde)

Abstract

A classification of the phase transition thresholds behind the Kirby Paris style independence results about Goodstein sequences and hydras is given. Moreover earlier phase transition results by Kent and Hodgson are improved. The article is intended to be suitable for teaching purposes and just requires basic familiarity with the standard classification of the provably recursive functions of PA and its fragments in terms of the Hardy functions.

Suggested Citation

  • Frederik Meskens & Andreas Weiermann, 2015. "Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games," Springer Books, in: Reinhard Kahle & Michael Rathjen (ed.), Gentzen's Centenary, edition 1, pages 455-478, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-10103-3_16
    DOI: 10.1007/978-3-319-10103-3_16
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