Speaker: 
James Cummings Associate Professor Department of Mathematical Sciences Carnegie Mellon University 

Title: 
Games, trees and sets


Abstract: 
I will prove the GaleStewart 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 selfcontained analysis of Namba forcing, including the proofs that it adds no reals under CH and is always stationarypreserving.