Max Aires, Rutgers University

Abstract

Everyone knows (hopefully) Ramsey's Theorem that 2-colorings of infinite graphs contain monochromatic subsets. In this talk, we investigate generalizations of this fact to general linear orders. We first discuss operations on linear orders, in particular generalizing general arithmetic (and ordinal arithmetic) to the larger class of all linear orders. Now define alpha->(beta, gamma)^2 as the property that all 2-colorings of graphs on (an order) alpha contain a 0-monochromatic beta or a 1-monochromatic beta. We shall investigate this property and see a number or positive and negative results.

See: https://sites.math.rutgers.edu/~kmg326/GCS/GCS.html