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Article Dans Une Revue Journal of Combinatorics Année : 2024

The reverse mathematics of Carlson's theorem for located words

Résumé

In this article, we give two proofs of Carlson's theorem for located words in~$\mathsf{ACA}^+_0$. 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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hal-04254970 , version 1 (23-10-2023)

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Tristan Bompard, Lu Liu, Ludovic Patey. The reverse mathematics of Carlson's theorem for located words. Journal of Combinatorics, In press. ⟨hal-04254970⟩
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