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)

  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.