Determinacy from scales
Organizers
Speaker
W. Hugh Woodin
Time
Wednesday, June 11, 2025 5:00 PM - 7:00 PM
Venue
A6-101
Online
Zoom 928 682 9093
(BIMSA)
Abstract
There have been many results showing in specific cases that determinacy is equivalent to its simplest structural consequences. One example from 30 years ago is that hyperprojective determinacy is equivalent to every hyperprojective set has a hyperprojective scale and that there is no uncountable hyperprojective set with a hyperprojective wellordering. This theorem, and its generalizations, are proved through an elaborate induction. For this reason a general equivalence theorem has always seemed out of reach. Our main result is exactly such a theorem. The new ingredients come from an emerging fine structure theory designed to handle the case of "long" extenders. This fine structure theory eliminates the need for an induction.
Speaker Intro
William Hugh Woodin is an American mathematician at Harvard University specializing in set theory. He has made many notable contributions to the theory of inner models and determinacy. A type of large cardinals, the Woodin cardinals, bears his name. He earned his Ph.D. from the University of California, Berkeley in 1984 under Robert M. Solovay. His dissertation title was Discontinuous Homomorphisms of C(Ω) and Set Theory. He served as chair of the Berkeley mathematics department for the 2002–2003 academic year. Woodin is a managing editor of the Journal of Mathematical Logic. He was elected a Fellow of the American Academy of Arts and Sciences in 2000 and elected to the National Academy of Sciences in 2023.