In this article, we prove that Ramsey's theorem for pairs and two colors is Π¹₁-conservative over~RCA₀ + BΣ⁰₂ + WF(ε₀) and over~RCA₀ + BΣ⁰₂ + ₙ WF(ω^ωₙ). These results improve theorems from Chong, Slaman and Yang and Ko{}odziejczyk and Yokoyama and belong to a long line of research towards the characterization of the first-order part of Ramsey's theorem for pairs.
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Houérou et al. (2024) studied this question.
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