Fernández-Duque, D, Shafer, P orcid.org/0000-0001-5386-9218 and Yokoyama, K (2020) Ekeland’s variational principle in weak and strong systems of arithmetic. Selecta Mathematica, 26 (5). 68. ISSN 1022-1824
Abstract
We analyze Ekeland’s variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to Π11- CA0, a strong theory of second-order arithmetic, while natural restrictions (e.g. to compact spaces or to continuous functions) yield statements equivalent to weak König’s lemma (WKL0) and to arithmetical comprehension (ACA0). We also find that the localized version of Ekeland’s variational principle is equivalent to Π11- CA0, even when restricted to continuous functions. This is a rare example of a statement about continuous functions having great logical strength.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. This is an open access article under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | Computability theory; Reverse mathematics; Second-order arithmetic; Variational principles |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Oct 2020 14:25 |
Last Modified: | 25 Jun 2023 22:28 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00029-020-00597-z |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:167164 |
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