From the 1 of 12 linked papers with an AI index.
12 papers
conservation of a Carlson-Simpson lemma for 1-variable words
Quentin Le Houérou, Ludovic Patey
The paper proves that adding the two‑color Carlson‑Simpson lemma for 1‑variable words to RCA₀ yields a Π⁰₄‑conservative extension of RCA₀ + BΣ₂, and uses this to show that several…
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…
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…
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 $…
Conservation of Ramsey's theorem for pairs and well-foundedness
Quentin Le Houérou, Ludovic Levy Patey, Keita Yokoyama
In this article, we prove that Ramsey's theorem for pairs and two colors is -conservative over~ and over~$\mathsf{RCA…