Ludovic Patey

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20142026

most citedSomewhere over the rainbow Ramsey theorem for pairs

10 citations · 68 across the 40 of their papers we have counts for

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Showing 2026 · math.LOShow all

8 papers · 2 filters

math.LO2026

The first-order part of the Ordered Variable Word theorem

Ludovic Patey

An ordered $ω$ -variable sequence over a finite alphabet~ $A$ is an infinite sequence over the extended alphabet $A ⊔ {x_{0}, x_{1}, \dots}$ , where each variable kind appears at…

math.LO2026

The weakness of typicality

Eric P. Astor, Laurent Bienvenu, Damir Dzhafarov +4

Many statements studied in reverse mathematics can be seen as mathematical problems, formulated in terms of instances and solutions. We develop a framework of typicality encompassi…

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

Hindman's theorem does not code $\emptyset^{(ω)}$ in one application

Lu Liu, Ludovic Patey

We prove that for every non-arithmetic set~ $C$ and every arithmetic finite coloring of~ $N$ , there is an infinite set $H \subseteq N$ whose non-empty finite sums o…

math.LO2026

The reverse mathematics of the Ordered Variable Word theorem

Lu Liu, Ludovic Patey

In this article, we study the reverse mathematics of variable word theorems used in the proof of the Dual Ramsey theorem. We prove that the Ordered Variable Word theorem does not i…

math.LO2026

Bounded Ramsey's theorem for triples in computability theory

Ludovic Patey, Paul Shafer

We study a restriction of Ramsey's theorem for 2-coloring of triples, in which homogeneous sets for color~1 are of bounded size ( $BRT_{2}^{3}$ ). We prove that the computationa…

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…

The first-order part of the Ordered Variable Word theorem

The weakness of typicality

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

Hindman's theorem does not code ∅(ω) in one application

The reverse mathematics of the Ordered Variable Word theorem

Bounded Ramsey's theorem for triples in computability theory

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

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

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

Hindman's theorem does not code $\emptyset^{(ω)}$ in one application

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