# Predicatively unprovable termination of the Ackermannian Goodstein process

@article{Arai2019PredicativelyUT, title={Predicatively unprovable termination of the Ackermannian Goodstein process}, author={Toshiyasu Arai and David Fern'andez-Duque and Stanley S. Wainer and Andreas Weiermann}, journal={Proceedings of the American Mathematical Society}, year={2019} }

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.

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