# The proof-theoretic strength of Ramsey's theorem for pairs and two colors.

@article{Patey2016ThePS,
title={The proof-theoretic strength of Ramsey's theorem for pairs and two colors.},
author={Ludovic Patey and K. Yokoyama},
journal={arXiv: Logic},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Logic
• Ramsey's theorem for $n$-tuples and $k$-colors ($\mathsf{RT}^n_k$) asserts that every k-coloring of $[\mathbb{N}]^n$ 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 $\mathsf{RT}^2_2$ is $\Pi^0_3$ conservative over $\mathsf{I}\Sigma^0_1$. This strengthens the proof of Chong, Slaman and Yang that $\mathsf{RT}^2_2$ does not imply $\mathsf{I}\Sigma^0_2$, and… CONTINUE READING
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