English

Fast Goodstein Walks

Logic 2022-05-17 v2

Abstract

We define a variant of the Goodstein process based on fast-growing functions and show that it terminates, but this fact is not provable in Kripke-Platek set theory or other theories of strength the Bachmann-Howard ordinal. 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.

Cite

@article{arxiv.2111.15328,
  title  = {Fast Goodstein Walks},
  author = {David Fernández-Duque and Andreas Weiermann},
  journal= {arXiv preprint arXiv:2111.15328},
  year   = {2022}
}
R2 v1 2026-06-24T07:57:34.780Z