Conservation of Ramsey’s theorem for pairs and well-foundedness
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In this article, we prove that Ramsey’s theorem for pairs and two colors is \( \Pi^1_1 \)-conservative over \(\mathsf{RCA}_0 + \mathsf{B}\Sigma_2^0 + \mathsf{WF}(\epsilon_0)\) and over \(\mathsf{RCA}_0 + \mathsf{B}\Sigma_2^0 + \bigcup_n \mathsf{WF}(\omega^\omega_n)\). These results improve theorems from Chong, Slaman and Yang and Kołodziejczyk and Yokoyama and belong to a long line of research towards the characterization of the first-order part of Ramsey’s theorem for pairs.
Recommended citation: Q. Le Houérou, L. Levy Patey and K. Yokoyama (2024). "Conservation of Ramsey's theorem for pairs and well-foundedness.".
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