A new ultrafilter proof of Van der Waerden's theorem
Logic
2026-03-05 v1 Combinatorics
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 , but contrarily to the other existing proofs, neither minimal nor idempotent ultrafilters are involved.
Keywords
Cite
@article{arxiv.2603.04043,
title = {A new ultrafilter proof of Van der Waerden's theorem},
author = {Mauro Di Nasso},
journal= {arXiv preprint arXiv:2603.04043},
year = {2026}
}