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}
}