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Is there an elementary proof of van der Waerden's theorem on arithmetic progressions using probabilistic methods?

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  • $\begingroup$ Do ultrafilters count as probabilistic? ;-) $\endgroup$
    – Monroe Eskew
    Commented Dec 13, 2023 at 7:40
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    $\begingroup$ Which proof of Szemeredi's theorem do you consider probabilistic? $\endgroup$
    – Thomas Bloom
    Commented Dec 13, 2023 at 8:46
  • $\begingroup$ There are for example probabilistic versions of regularity lemma and so on. See for example https://arxiv.org/abs/1410.5966 $\endgroup$
    – Mohammad Golshani
    Commented Dec 13, 2023 at 16:29

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