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arXiv · 1906.00020

Predicatively unprovable termination of the Ackermannian Goodstein process

Toshiyasu Arai·David Fernández-Duque·Stanley Wainer·Andreas Weiermann
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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.

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Toshiyasu Arai, David Fernández-Duque, Stanley Wainer, Andreas Weiermann. 2019-05-31. Predicatively unprovable termination of the Ackermannian Goodstein process. https://arxiv.org/abs/1906.00020

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