English

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 Π11\Pi^1_1-bar induction. The equivalence was proved over ACA0\mathbf{ACA_0}, 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 Π11\Pi^1_1-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}
}
R2 v1 2026-06-23T09:38:23.533Z