Predicatively unprovable termination of the Ackermannian Goodstein process
Logic
2019-06-04 v1
Abstract
The classical Goodstein process gives rise to long but finite sequences of natural numbers whose termination is not provable in Peano arithmetic. In this manuscript we consider a variant based on the Ackermann function. We show that Ackermannian Goodstein sequences eventually terminate, but this fact is not provable using predicative means.
Cite
@article{arxiv.1906.00020,
title = {Predicatively unprovable termination of the Ackermannian Goodstein process},
author = {Toshiyasu Arai and David Fernández-Duque and Stanley Wainer and Andreas Weiermann},
journal= {arXiv preprint arXiv:1906.00020},
year = {2019}
}