Frittaion, E orcid.org/0000-0003-4965-9271 and Patey, L (2017) Coloring the rationals in reverse mathematics. Computability, 6 (4). pp. 319-331. ISSN 2211-3568
Abstract
Ramsey’s theorem for pairs asserts that every 2-coloring of the pairs of integers has an infinite monochromatic subset. In this paper, we study a strengthening of Ramsey’s theorem for pairs due to Erdős and Rado, which states that every 2-coloring of the pairs of rationals has either an infinite 0-homogeneous set or a 1-homogeneous set of order type η, where η is the order type of the rationals. This theorem is a natural candidate to lie strictly between the arithmetic comprehension axiom and Ramsey’s theorem for pairs. This Erdős–Rado theorem, like the tree theorem for pairs, belongs to a family of Ramsey-type statements whose logical strength remains a challenge.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 – IOS Press and the author. This is an author produced version of a paper published in Computability. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at IOS Press through https://doi.org/10.3233/COM-160067 |
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 12:01 |
Last Modified: | 22 Nov 2018 12:01 |
Status: | Published |
Publisher: | IOS Press |
Identification Number: | 10.3233/COM-160067 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:138942 |