10 papers · 1 filter
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~, there is an infinite -variable word on which all the 1-variable wor…
Largeness notions and polytime translation for -consequences of
Quentin Le Houérou, Ludovic Patey
Le Houérou, Patey and Yokoyama defined a parameterized version of -largeness to prove that is a -conservative extension of $\ma…
Partition theorems for Ketonen-Solovay largeness: Hardy-like version
Quentin Le Houérou, Ludovic Patey
We develop the framework of -largeness introduced by Ketonen and Solovay, by proving a partition theorem for -large sets with which generalizes theorems from Ketonen…
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 $…
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 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…