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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Independence of Ramsey theorem variants using $\varepsilon _0$
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by Harvey Friedman and Florian Pelupessy PDF
Proc. Amer. Math. Soc. 144 (2016), 853-860 Request permission

Abstract:

We show that Friedman’s finite adjacent Ramsey theorem is unprovable in Peano Arithmetic, and give a new proof of the unprovability of the Paris–Harrington theorem in $\mathrm {PA}$. We also determine the status of these theorems for each dimension. It is to be noted that the finite adjacent Ramsey theorem for dimension $d$ is equivalent to the Paris–Harrington theorem for dimension $d+1$.
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Additional Information
  • Harvey Friedman
  • Affiliation: Department of Mathematics, Ohio State University, Room 754, Mathematics Building, 231 West 18th Avenue, Columbus, Ohio 43210
  • MR Author ID: 69465
  • Email: friedman@math.ohio-state.edu
  • Florian Pelupessy
  • Affiliation: Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan
  • Email: florian.pelupessy@operamail.com
  • Received by editor(s): February 8, 2013
  • Received by editor(s) in revised form: January 19, 2015
  • Published electronically: June 26, 2015
  • Additional Notes: This research was partially supported by the John Templeton Foundation grant ID #36297 and an Ohio State University Presidential Research Grant. The opinions expressed here are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
  • Communicated by: Mirna DĹľamonja
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 853-860
  • MSC (2010): Primary 03F30; Secondary 03F15, 03D20, 05C55
  • DOI: https://doi.org/10.1090/proc12759
  • MathSciNet review: 3430859