Infinitary Hales-Jewett theorem. Another proof

TL;DR

This paper presents a new proof of the infinitary Hales-Jewett theorem that avoids ultrafilters, offering an alternative approach to a fundamental result in combinatorics.

Contribution

It provides a novel proof technique for the infinitary Hales-Jewett theorem without ultrafilters, expanding the methodological toolkit in combinatorics.

Findings

Proof of the infinitary Hales-Jewett theorem without ultrafilters

Alternative combinatorial proof approach

Potential implications for related combinatorial theorems

Abstract

We give a proof of an infinitary version of the well known Hales-Jewett theorem on finite words avoiding the use of ultrafilters.