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The reverse mathematics of Carlson's theorem for located words

Combinatorics 2022-08-08 v1 Logic

Abstract

In this article, we give two proofs of Carlson's theorem for located words in~ACA0+\mathsf{ACA}^+_0. The first proof is purely combinatorial, in the style of Towsner's proof of Hindman's theorem. The second uses topological dynamics to show that an iterated version of Hindman's theorem for bounded sums implies Carlson's theorem for located words.

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Cite

@article{arxiv.2208.03152,
  title  = {The reverse mathematics of Carlson's theorem for located words},
  author = {Tristan Bompard and Lu Liu and Ludovic Patey},
  journal= {arXiv preprint arXiv:2208.03152},
  year   = {2022}
}

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16 pages