Thursday, May 2 from 1:30 to 2:30pm
Speaker: Shehzad Ahmed
Title: Borel determinacy
Abtract: We have seen various determinacy results throughout the semester, all of which have required large cardinal hypotheses. So, it seems natural to see how much determinacy we can get in ZFC. It turns out that we can get quite a bit of determinacy out of the standard axioms, and in fact we see that most sets that the analyst would encounter on a regular basis are determined. With that said, we will go through a high level sketch of Martin’s inductive proof of Borel Determinacy. Our interest here is in the result itself, the elegance of the proof, and the machinery of covering games and unravelings. Time permitting, I will mention applications of Borel Determinacy, as well as other uses of covering games.