Combinatorial set theory

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

Cummings proposes a program of research in combinatorial set theory. Infinite graphs, trees and orderings are the main objects of research in this program. The proposed research uses a wide range of techniques including forcing, PCF theory and inner model theory. The immediate goal of Cummings' research program is to get a better understanding of certain infinite mathematical structures. Problems about these structures arise in many areas of mathematics including algebra, analysis, topology and (perhaps surprisingly) the study of finite structures. The long term goal is to forge new tools for the construction and analysis of infinite structures, which should then find broader application.