4 citations · 4 across the 5 of their papers we have counts for
5 papers
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…
Primitive recursive reverse mathematics
Nikolay Bazhenov, Marta Fiori-Carones, Lu Liu +1
We use a second-order analogy of to investigate the proof-theoretic strength of theorems in countable algebra, analysis, and infinite combinatorics.…
The reverse mathematics of Carlson's theorem for located words
Tristan Bompard, Lu Liu, Ludovic Patey
In this article, we give two proofs of Carlson's theorem for located words in~. The first proof is purely combinatorial, in the style of Towsner's proof of Hindma…
Carlson-Simpson's lemma and applications in reverse mathematics
Paul-Elliot Anglès d'Auriac, Bastien Mignoty, Lu Liu +1
We study the reverse mathematics of infinitary extensions of the Hales-Jewett theorem, due to Carlson and Simpson. These theorems have multiple applications in Ramsey's theory, suc…