Metric fixed point theory and partial impredicativity-Reference-Cited by-同舟云学术

Metric fixed point theory and partial impredicativity

Published:2023-04-10 Issue:2248 Volume:381 Page:
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Fernández-Duque D.¹²^ORCID,Shafer P.³,Towsner H.⁴,Yokoyama K.⁵

Affiliation:

1. Department of Mathematics WE16, Ghent University, Ghent, Belgium

2. Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

3. School of Mathematics, University of Leeds, Leeds, West Yorkshire, UK

4. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, USA

5. Mathematical Institute, Tohoku University, Sendai, Miyagi, Japan

Abstract

We show that the Priess-Crampe & Ribenboim fixed point theorem is provable inRCA0. 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 betweenATR0andΠ11-CA0. We also exhibit several weakenings of Caristi’s theorem that are equivalent toWKL0and toACA0.This article is part of the theme issue ‘Modern perspectives in Proof Theory’.

Funder

National Science Foundation

Engineering and Physical Sciences Research Council

John Templeton Foundation

Fonds Wetenschappelijk Onderzoek

Japan Society for the Promotion of Science

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2022.0012