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.
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The second author has used the main results of this paper repeatedly during lectures on selected chapters from proof theory.
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Acknowledgements
The second author’s research has been supported in part by the John Templeton Foundation and by the Flemish Research Organization FWO.
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Meskens, F., Weiermann, A. (2015). Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games. In: Kahle, R., Rathjen, M. (eds) Gentzen's Centenary. Springer, Cham. https://doi.org/10.1007/978-3-319-10103-3_16
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DOI: https://doi.org/10.1007/978-3-319-10103-3_16
Publisher Name: Springer, Cham
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