Metric fixed point theory and partial impredicativity

0572031 - ÚI 2024 RIV GB eng J - Článek v odborném periodiku
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
Institucionální podpora: RVO:67985807
Klíčová slova: computability theory * reverse mathematics * second-order arithmetic * fixed-point theorems * variational principles
Obor OECD: Pure mathematics
Impakt faktor: 5, rok: 2022
Způsob publikování: Omezený přístup
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'.
Trvalý link: https://hdl.handle.net/11104/0342867


Vědecká data: Preprint at ArXiv.org