Quentin Le Houérou

collaborators

3 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.LO2024

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…

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

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

Ramsey-like theorems for the Schreier barrier

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

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