Frittaion, E orcid.org/0000-0003-4965-9271 (2017) Brown’s lemma in second-order arithmetic. Fundamenta Mathematicae, 238 (3). pp. 269-283. ISSN 0016-2736
Abstract
Brown’s lemma states that in every finite coloring of the natural numbers there is a homogeneous piecewise syndetic set. We show that Brown’s lemma is equivalent to IΣ02 over RCA∗0. We show in contrast that (infinite) van der Waerden’s theorem is equivalent to BΣ02 over RCA∗0. We finally consider the finite version of Brown’s lemma and show that it is provable in RCA0 but not in RCA∗0.
Metadata
Item Type: | Article |
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Authors/Creators: |
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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: | 22 Nov 2018 12:43 |
Last Modified: | 22 Nov 2018 12:43 |
Status: | Published |
Publisher: | Polish Academy of Sciences |
Identification Number: | 10.4064/fm221-9-2016 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138944 |
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