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


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.