10 citations · 68 across the 40 of their papers we have counts for
8 papers · 2 filters
Controlling iterated jumps of solutions to combinatorial problems
Ludovic Patey
Among the Ramsey-type hierarchies, namely, Ramsey's theorem, the free set, the thin set and the rainbow Ramsey theorem, only Ramsey's theorem is known to collapse in reverse mathem…
Coloring the rationals in reverse mathematics
Emanuele Frittaion, Ludovic Patey
Ramsey's theorem for pairs asserts that every 2-coloring of the pairs of integers has an infinite monochromatic subset. In this paper, we study a strengthening of Ramsey's theorem…
Open questions about Ramsey-type statements in reverse mathematics
Ludovic Patey
Ramsey's theorem states that for any coloring of the n-element subsets of N with finitely many colors, there is an infinite set H such that all n-element subsets of H have the same…
Dominating the Erdos-Moser theorem in reverse mathematics
Ludovic Patey
The Erdos-Moser theorem (EM) states that every infinite tournament has an infinite transitive subtournament. This principle plays an important role in the understanding of the comp…
The strength of the tree theorem for pairs in reverse mathematics
Ludovic Patey
No natural principle is currently known to be strictly between the arithmetic comprehension axiom (ACA) and Ramsey's theorem for pairs (RT^2_2) in reverse mathematics. The tree the…
The weakness of being cohesive, thin or free in reverse mathematics
Ludovic Patey
Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this paper, we investigate the lack of robustness of Ramsey's…