Reverse mathematics and a Ramsey-type König's Lemma

Abstract

In this paper, we propose a weak regularity principle which is similar to both weak König'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.

8 pages, 1 figure. This version includes a number of small expository changes. More significantly, Yokoyama Keita answered a question from the previous version, and has generously allowed me to include his proof (Statement 15-Question 19)