Series: Penn State Logic Seminar Date: Wednesday, June 2, 2004 Time: 11:10 AM - 12:25 PM Place: 311 Boucke Building Speaker: Carl Mummert, Penn State, Mathematics Title: Borel Determinacy (part 1) Abstract: To begin a certain game, two opponents agree on a subset of the unit interval. They then take turns calling out successive binary digits to determine a real number in the interval. Player I wins if the number determined by the two players is in the chosen subset; player II wins otherwise. In this talk, I will prove that if the chosen subset is a Borel subset of the unit interval then one of the two players has a winning strategy for this game. This result, known as Borel Determinacy, was obtained by Martin in the 1970s. Before this result was established, Friedman showed that any proof of Borel Determinacy must require many iterations of the powerset operator. If time permits, I will briefly discuss Friedman's result.