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  1. Goodstein Sequences Based on a Parametrized Ackermann–Péter Function.Toshiyasu Arai, Stanley S. Wainer & Andreas Weiermann - 2021 - Bulletin of Symbolic Logic 27 (2):168-186.
    Following our [6], though with somewhat different methods here, further variants of Goodstein sequences are introduced in terms of parameterized Ackermann–Péter functions. Each of the sequences is shown to terminate, and the proof-theoretic strengths of these facts are calibrated by means of ordinal assignments, yielding independence results for a range of theories: PRA, PA,$\Sigma ^1_1$-DC$_0$, ATR$_0$, up to ID$_1$. The key is the so-called “Hardy hierarchy” of proof-theoretic bounding finctions, providing a uniform method for associating Goodstein-type sequences with parameterized normal (...)
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  • Pure Σ2-elementarity beyond the core.Gunnar Wilken - 2021 - Annals of Pure and Applied Logic 172 (9):103001.
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