Conservation of Ramsey's theorem for pairs and well-foundedness

2024/02/18 by Houérou, Quentin Le, Patey, Ludovic Levy, Yokoyama, Keita · 2 citations
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2402.11616

Abstract

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 + \bigcup_n WF(ω^ω_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.

Cited by

• The reverse mathematics of bounded Ramsey's theorem for pairs
• Finite Combinatorics and Fragments of Arithmetic

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