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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/16703

Title: The proof-theoretic strength of Ramsey's theorem for pairs and two colors
Authors: Patey, Ludovic
Yokoyama, Keita
Keywords: Reverse Mathematics
Ramsey’s theorem
proof-theoretic strength
Issue Date: 2018-07-21
Publisher: Elsevier
Magazine name: Advances in Mathematics
Volume: 330
Start page: 1034
End page: 1070
DOI: 10.1016/j.aim.2018.03.035
Abstract: Ramsey's theorem for n-tuples and k-colors (RT^n_k) asserts that every k-coloring of [N]^n admits an infinite monochromatic subset. We study the proof-theoretic strength of Ramsey's theorem for pairs and two colors, namely, the set of its Pi^0_1 consequences, and show that RT^2_2 is Pi^0_3 conservative over ISigma^0_1. This strengthens the proof of Chong, Slaman and Yang that RT^2_2 does not imply ISigma^0_2, and shows that RT^2_2 is finitistically reducible, in the sense of Simpson's partial realization of Hilbert's Program. Moreover, we develop general tools to simplify the proofs of Pi^0_3-conservation theorems.
Rights: Copyright (C)2018, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license (CC BY-NC-ND 4.0). [http://creativecommons.org/licenses/by-nc-nd/4.0/] NOTICE: This is the author's version of a work accepted for publication by Elsevier. Ludovic Patey, Keita Yokoyama, Advances in Mathematics, 330, 2018, 1034-1070, http://dx.doi.org/10.1016/j.aim.2018.03.035
URI: http://hdl.handle.net/10119/16703
Material Type: author
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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