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.
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Acknowledgements
The first author was supported by a scholarship from the University of Leeds (“University of Leeds 110th Anniversary Scholarship”).
The second author was supported by a grant from the John Templeton Foundation (“A new dawn of intuitionism: mathematical and philosophical advances”, ID 60842) (The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.).
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Krombholz, M., Rathjen, M. (2020). Upper Bounds on the Graph Minor Theorem. In: Schuster, P., Seisenberger, M., Weiermann, A. (eds) Well-Quasi Orders in Computation, Logic, Language and Reasoning. Trends in Logic, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-30229-0_6
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DOI: https://doi.org/10.1007/978-3-030-30229-0_6
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