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2024-12-01

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cc by (c) Fernández Duque, David et al., 2024
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228957

Fast Goodstein walks

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https://doi.org/10.1112/blms.13210

Abstract

We introduce a family ( ) < of fast-growing functions based on 0 and use these to define a variant of the Goodstein process. We show that this variant terminates and that this fact is not provable in Kripke–Platek set theory (or other theories of Bachmann–Howard strength). We, moreover, show that this Goodstein process is of maximal length, so that any alternative Goodstein process based on the same fast-growing functions will also terminate.

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Filosofia, Teoria de conjunts, Lògica matemàtica

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Philosophy, Set theory, Mathematical logic

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FERNÁNDEZ DUQUE, David and WEIERMANN, Andreas. Fast Goodstein walks. Bulletin of the London Mathematical Society. 2024. ISSN 0024-6093. [consulted: 7 of June of 2026]. Available at: https://hdl.handle.net/2445/228957

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