How strong are single fixed points of normal functions?
Logic
2021-07-07 v2
Abstract
In a recent paper by M. Rathjen and the present author it has been shown that the statement ``every normal function has a derivative'' is equivalent to -bar induction. The equivalence was proved over , for a suitable representation of normal functions in terms of dilators. In the present paper we show that the statement ``every normal function has at least one fixed point'' is equivalent to -induction along the natural numbers.
Cite
@article{arxiv.1906.00645,
title = {How strong are single fixed points of normal functions?},
author = {Anton Freund},
journal= {arXiv preprint arXiv:1906.00645},
year = {2021}
}