Krombholz, M and Rathjen, M (2020) Upper Bounds on the Graph Minor Theorem. In: Schuster, P, Seisenberger, M and Weiermann, A, (eds.) Well-Quasi Orders in Computation, Logic, Language and Reasoning: A Unifying Concept of Proof Theory, Automata Theory, Formal Languages and Descriptive Set Theory. Well Quasi-Orders in Computer Science (Dagstuhl Seminar 16031), 17-22 Jan 2016, Dagstuhl, Germany. Trends in Logic, 53 . Springer , pp. 145-160. ISBN 978-3-030-30228-3
Abstract
Lower bounds on the proof-theoretic strength of the graph minor theorem were found over 30 years ago by Friedman, Robertson and Seymour (Metamathematics of the graph minor theorem, pp 229–261, [4]), but upper bounds have always been elusive. We present recently found upper bounds on the graph minor theorem and other theorems appearing in the Graph Minors series. Further, we give some ideas as to how the lower bounds on some of these theorems might be improved.
Metadata
Item Type: | Proceedings Paper |
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Copyright, Publisher and Additional Information: | © Springer Nature Switzerland AG 2020. This version of the chapter vhas been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/978-3-030-30229-0_6. |
Keywords: | Proof theory; Graph Minor Theorem |
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) |
Funding Information: | Funder Grant number John Templeton Foundation (US) 60842 |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Jul 2019 16:29 |
Last Modified: | 16 Feb 2024 04:07 |
Status: | Published |
Publisher: | Springer |
Series Name: | Trends in Logic |
Identification Number: | 10.1007/978-3-030-30229-0_6 |
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Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147992 |