Ramsey’s Theorem applied to infinite traceable graphs
University of Connecticut
We consider three applications of Ramsey’s Theorem to infinite traceable graphs and finitely generated lattices from the point of view of reverse mathematics. For two of the applications, we will show that Ramsey’s Theorem is necessary while for the third application, it is not necessary. We will conclude with some related open questions.
Reed Solomon is a Professor in the Department of Mathematics at the University of Connecticut, studying computability theory. He received his doctorate from Cornell University in 1998, under the supervision of Richard Shore, and subsequently held postdoctoral positions at the University of Wisconsin and Notre Dame University.