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math.LO2025
The reverse mathematics of bounded Ramsey's theorem for pairs
Quentin Le Houérou, Ludovic Patey
In this article, we study a degenerate version of Ramsey's theorem for pairs and two colors (), in which the homogeneous sets for color 1 are of bounded size. By $…
math.LO2025
Ramsey-like theorems and immunities
Ahmed Mimouni, Ludovic Patey
A Ramsey-like theorem is a statement of the form ``For every 2-coloring of , there exists an infinite set~ such that avoids some pat…
math.LO2025
Ramsey-like theorems for separable permutations
Quentin Le Houérou, Ludovic Patey
We conduct a computability-theoretic study of Ramsey-like theorems of the form "Every coloring of the edges of an infinite clique admits an infinite sub-clique avoiding some patter…