10 citations · 68 across the 40 of their papers we have counts for
53 papers
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…
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…
Hindman's theorem does not code in one application
Lu Liu, Ludovic Patey
We prove that for every non-arithmetic set~ and every arithmetic finite coloring of~, there is an infinite set whose non-empty finite sums o…
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…
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 (). We prove that the computationa…
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…