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This article proves a conservative extension of Ramsey's theorem for pairs, suggesting further advancements in logic.
In this article, we prove that Ramsey's theorem for pairs and two colors is a conservative extension of , where a formula consists of a universal quantifier over sets followed by a formula. The proof is an improvement of a result by Patey and Yokoyama and a step toward the resolution of the longstanding question of the first‐order part of Ramsey's theorem for pairs. For this, we introduce a new general technique for proving ‐conservation theorems.
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Houérou et al. (2026) studied this question.
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