Metric fixed point theory and partial impredicativity

0572031 - ÚI 2024 RIV GB eng J - Journal Article
Fernández-Duque, David - Shafer, P. - Towsner, H. - Yokoyama, K.
Metric fixed point theory and partial impredicativity.
Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences. Roč. 381, č. 2248 (2023), č. článku 20220012. ISSN 1364-503X. E-ISSN 1471-2962
Institutional support: RVO:67985807
Keywords : computability theory * reverse mathematics * second-order arithmetic * fixed-point theorems * variational principles
OECD category: Pure mathematics
Impact factor: 5, year: 2022
Method of publishing: Limited access
https://dx.doi.org/10.1098/rsta.2022.0012

We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in RCA0. Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel functions is equivalent to the transfinite leftmost path principle, which falls strictly between ATR0 and p11-CA0. We also exhibit several weakenings of Caristi's theorem that are equivalent to WKL0 and to ACA0.This article is part of the theme issue 'Modern perspectives in Proof Theory'.
Permanent Link: https://hdl.handle.net/11104/0342867


Research data: Preprint at ArXiv.org