Metric fixed point theory and partial impredicativity

Authors: David Fernández-Duque, P. Shafer, H. Towsner, K. Yokoyama
Publication year: 2023
Publication type: Článek v odborném periodiku
Periodical: Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences
Bibliographic citation: 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. 2023, 381(2248), 20220012. ISSN 1364-503X. E-ISSN 1471-2962
Dostupné z: doi:10.1098/rsta.2022.0012.
DOI: 10.1098/rsta.2022.0012
ID: 572031
Online record: View online record

Abstract

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'.