Department of Mathematical Sciences
Carnegie Mellon University
Games, trees and sets
I will prove the Gale-Stewart theorem on the determinacy of open sets, and explain how Shelah used this to prove partition theorems about infinite trees. I will then discuss forcing posets in which the conditions are infinite trees, and will describe how to analyse them using games and partition theorems. In particular I will give a self-contained analysis of Namba forcing, including the proofs that it adds no reals under CH and is always stationary-preserving.