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4 papers · 1 filter
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…
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…
conservation of Ramsey's theorem for pairs
Quentin Le Houérou, Ludovic Levy Patey, Keita Yokoyama
In this article, we prove that Ramsey's theorem for pairs and two colors is a conservative extension of , where a $\forall Î ^0_…
Ramsey-like theorems for the Schreier barrier
Lorenzo Carlucci, Oriola Gjetaj, Quentin Le Houérou +1
The family of finite subsets of the natural numbers such that is known as the Schreier barrier in combinatorics and Banach Space theory, and as the family of exa…