Quentin Le Houérou

activity

20242026

most citedRamsey-like theorems for the Schreier barrier

1 citations · 1 across the 9 of their papers we have counts for

collaborators

10 papers

math.LO2026

$Π_{4}^{0}$ conservation of a Carlson-Simpson lemma for 1-variable words

Quentin Le Houérou, Ludovic Patey

Carlson and Simpson proved that for every finite coloring of the 1-variable words over a finite alphabet~ $A$ , there is an infinite $ω$ -variable word on which all the 1-variable wor…

math.LO2026

Largeness notions and polytime translation for $\forall Σ_{3}^{0}$ -consequences of $RT_{2}^{2}$

Quentin Le Houérou, Ludovic Patey

Le Houérou, Patey and Yokoyama defined a parameterized version of $α$ -largeness to prove that $WKL_{0} + RT_{2}^{2}$ is a $\forall Σ_{3}^{0}$ -conservative extension of $\ma…

math.LO2026

Partition theorems for Ketonen-Solovay largeness: Hardy-like version

Quentin Le Houérou, Ludovic Patey

We develop the framework of $α$ -largeness introduced by Ketonen and Solovay, by proving a partition theorem for $α$ -large sets with $α < ε_{0}$ which generalizes theorems from Ketonen…

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 ( $RT_{2}^{2}$ ), in which the homogeneous sets for color 1 are of bounded size. By $…

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…

math.LO2024★ 1 cited

Ramsey-like theorems for the Schreier barrier

Lorenzo Carlucci, Oriola Gjetaj, Quentin Le Houérou +1

The family of finite subsets $s$ of the natural numbers such that $∣ s ∣ = 1 + min s$ is known as the Schreier barrier in combinatorics and Banach Space theory, and as the family of exa…

math.LO2024

The reverse mathematics of the pigeonhole hierarchy

Quentin Le Houérou, Ludovic Levy Patey, Ahmed Mimouni

The infinite pigeonhole principle for $k$ colors ( $RT_{k}^{1}$ ) states, for every $k$ -partition $A_{0} ⊔ \dots ⊔ A_{k - 1} = N$ , the existence of an infinite su…

math.LO2024

$Π_{4}^{0}$ 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 $\forall Π_{4}^{0}$ conservative extension of $RCA_{0} + B Σ_{2}^{0}$ , where a $\forall Π_{4}^{0}$ …

math.LO2024

$Π_{4}^{0}$ conservation of the Ordered Variable Word theorem

Quentin Le Houérou, Ludovic Levy Patey

A left-variable word over an alphabet~ $A$ is a word over~ $A \cup {⋆}$ whose first letter is the distinguished symbol~ $⋆$ standing for a placeholder. The Ordered Variable…

math.LO2024

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 $Π_{1}^{1}$ -conservative over~ $RCA_{0} + B Σ_{2}^{0} + WF (ε_{0})$ and over~$\mathsf{RCA}_0…

Π40​ conservation of a Carlson-Simpson lemma for 1-variable words

Largeness notions and polytime translation for ∀Σ30​-consequences of RT22​

Partition theorems for Ketonen-Solovay largeness: Hardy-like version

The reverse mathematics of bounded Ramsey's theorem for pairs

Ramsey-like theorems for separable permutations

Ramsey-like theorems for the Schreier barrier

The reverse mathematics of the pigeonhole hierarchy

Π40​ conservation of Ramsey's theorem for pairs

Π40​ conservation of the Ordered Variable Word theorem

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

$Π_{4}^{0}$ conservation of a Carlson-Simpson lemma for 1-variable words

Largeness notions and polytime translation for $\forall Σ_{3}^{0}$ -consequences of $RT_{2}^{2}$

$Π_{4}^{0}$ conservation of Ramsey's theorem for pairs

$Π_{4}^{0}$ conservation of the Ordered Variable Word theorem