Infinite trees and partition relations

Infinite trees and partition calculus (aka, Ramsey theory) are well-known to be intertwined. For instance, Ramsey theorem implies Konig's lemma that asserts that every infinite tree which is finitely branching has an infinite path.
In this talk, we shall deal with uncountable trees such as Souslin trees and Aronszajn trees, and show how to derive negative partition relations from them.
 

Lecture notes.