Reverse mathematics and a Ramsey-type K\"onig's Lemma

TL;DR

This paper introduces a weak regularity principle akin to weak K"onig's lemma and Ramsey's theorem, analyzing its computational strength and exploring various generalizations within reverse mathematics.

Contribution

It proposes a new weak regularity principle and studies its computational strength and potential generalizations in reverse mathematics.

Findings

The principle has a specific computational strength profile.

Different generalizations exhibit varied logical strengths.

The study advances understanding of weak regularity principles in reverse mathematics.

Abstract

In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.