A new ultrafilter proof of Van der Waerden's theorem

Mauro Di Nasso

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arXiv · 2603.04043

A new ultrafilter proof of Van der Waerden's theorem

Mauro Di Nasso

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Abstract

We present a new short proof of Van der Waerden's Theorem about the existence of arbitrarily long monochromatic arithmetic progressions. The proof uses algebra in the compact space of ultrafilters $\beta\N$, but contrarily to the other existing proofs, neither minimal nor idempotent ultrafilters are involved.

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Mauro Di Nasso. 2026-03-04. A new ultrafilter proof of Van der Waerden's theorem. https://arxiv.org/abs/2603.04043

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