From the 1 of 8 linked papers with an AI index.
1 citations · 1 across the 5 of their papers we have counts for
8 papers
conservation of a Carlson-Simpson lemma for 1-variable words
Quentin Le Houérou, Ludovic Patey
The paper proves that adding the two‑color Carlson‑Simpson lemma for 1‑variable words to RCA₀ yields a Π⁰₄‑conservative extension of RCA₀ + BΣ₂, and uses this to show that several…
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…
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 $…
Conservation of Ramsey's theorem for pairs and well-foundedness
Quentin Le Houérou, Ludovic Levy Patey, Keita Yokoyama
In this article, we prove that Ramsey's theorem for pairs and two colors is -conservative over~ and over~$\mathsf{RCA…
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…