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The reverse mathematics of Carlson's theorem for located words
Published 5 Aug 2022 in math.CO and math.LO | (2208.03152v1)
Abstract: 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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