Classifying Phase Transition Thresholds for Goodstein Sequences and Hydra Games

Frederik Meskens () and Andreas Weiermann ()
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Frederik Meskens: Gent Universitet, Vakgroep Wiskunde
Andreas Weiermann: Gent Universitet, Vakgroep Wiskunde

A chapter in Gentzen's Centenary, 2015, pp 455-478 from Springer

Abstract: 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.

Keywords: Goodstein Sequence; Phase Transition Threshold; Step Counting Function; Sharp Threshold Function; Superprocesses (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10103-3_16

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DOI: 10.1007/978-3-319-10103-3_16

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