check
Set Theory Seminar: Alejandro Poveda (HUJI) - The failure of the Galvin property at successors of singulars | Einstein Institute of Mathematics

Set Theory Seminar: Alejandro Poveda (HUJI) - The failure of the Galvin property at successors of singulars

Date: 
Wed, 23/03/202214:00-16:00
Repeats every week every Wednesday 2 times
Location: 
Ross 70
Title:
The failure of the Galvin property at successors of singulars.
 
Abstract:

The primary goal of these lectures is to present the proof of the following result: Assuming the existence of a supercompact cardinal there is a model of ZFC where Galvin’s property fails at the successor of every singular cardinal, simultaneously. 

In the upcoming session, we plan to revisit the results thus far presented by S. Garti and describe the challenges involved in producing failures of Galvin’s property at accessible cardinals; such as \aleph_{\omega+1}. Once this is accomplished we will move forward and comment on the main ideas behind the proof of the theorem. Our main forcing-theoretic tool will be the so-called Radin forcing with interleaved collapses. A more sophisticated version of this forcing appeared in work by Foreman & Woodin; instead, our approach will follow Cummings’ later exposition. We will describe the forcing taking for granted the existence of guiding generics. Once the exposition of the poset is accomplished we shall show how to produce such guiding generics in the absence of GCH. We plan to conclude our talks by proving the theorem and (if time permits) presenting some relevant open problems.


Join Zoom Meeting
https://huji.zoom.us/j/81672724380?pwd=VXcxQWw5aHpzNkp2ZUk5amtDMTc0Zz09

Meeting ID: 816 7272 4380
Passcode: 998395