| Speaker: |
James Cummings Associate Professor Department of Mathematical Sciences Carnegie Mellon University |
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| Title: |
Games, trees and sets
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| Abstract: |
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.