Series: Penn State Logic Seminar Date: Tuesday, February 4, 2003 Time: 2:30 - 3:45 PM Place: 220 Hammond Building Speaker: Ernest Schimmerling, CMU, Mathematics Title: Precipitous Ideals and Collapsing Functions Abstract: If V = L then there are no precipitous ideal on omega_1. Velickovic refined the proof of this fact and abstracted from it the notion of a collapsing function for a cardinal lambda, where in his proof lambda = omega_3. I will talk about a characterization of those lambda which carry collapsing functions in terms of what might be a new Erdos property on lambda. The characterization is in models of form L[E] where E is a coherent sequence of extenders. A corollary is that the existence of a Woodin limit of Woodin cardinals is consistent with the non-existence of a precipitous ideal on omega_1. It is a well-known open problem whether such corollaries can be obtained by forcing. These are modest results but they provide a nice segue into the basics of inner model theory. Most of the definitions will be provided as well as some of the proofs.