Using ultrafilters to prove Ramsey-type theorems

DOI10.1080/00029890.2022.2004848arXiv1711.01304WikidataQ113853667 ScholiaQ113853667MaRDI QIDQ6293462

Publication date: 3 November 2017

Abstract: Ultrafilters are a tool, originating in mathematical logic and general topology, that has steadily found more and more uses in multiple areas of mathematics, such as combinatorics, dynamics, and algebra, among others. The purpose of this article is to introduce ultrafilters in a friendly manner and present some applications to the branch of combinatorics known as Ramsey theory, culminating with a new ultrafilter-based proof of van der Waerden's theorem.

Mathematics Subject Classification ID

Ramsey theory (05D10) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80)

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