Adjacent Ramsey theory and Higman's lemma

TL;DR

This paper presents a concise proof of Higman's lemma leveraging Friedman's adjacent Ramsey theorem, offering an alternative approach to understanding its reverse mathematical complexity.

Contribution

It introduces a novel proof technique connecting adjacent Ramsey theory with Higman's lemma, simplifying the existing proof and clarifying its logical strength.

Findings

Provides a shorter proof of Higman's lemma

Establishes an alternative proof for the upper bound in reverse mathematics

Connects adjacent Ramsey theory with combinatorial principles

Abstract

We show a short proof of Higman's lemma using Friedman's adjacent Ramsey theorem for pairs. This provides an alternative proof of the known upper bound for the reverse mathematical status of Higman's lemma and that of its miniaturised version.