Fast Goodstein walks

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-12-27 DOI:10.1112/blms.13210

David Fernández-Duque, Andreas Weiermann

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引用次数: 0

Abstract

We introduce a family ${(A_{k})}_{k < ω}$ of fast-growing functions based on $ε_{0}$ 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.