Higher Chang Conjecture

Seminar
Speaker
Yait Hayut (HUJI)
Date
04/11/2020 - 16:00 - 14:00Add to Calendar 2020-11-04 14:00:00 2020-11-04 16:00:00 Higher Chang Conjecture In this talk I will present some results regarding the consistency strength of Higher variants of Chang's Conjecture.  I will start with the classical result by Silver of Chang's Conjecture from $\omega_1$-Erdos cardinal.   Then, I will give an upper bound for the consistency strength of  $(\aleph_{\omega+1}, \aleph_{\omega}) -->>(\aleph_1, \aleph_0)$ and $(\aleph_4, \aleph_3) -->> (\aleph_2, \aleph_1)$ (joint with Eskew) from supercompactness assumptions.  If time permits, I will describe the strategy for obtaining a global result: (\kappa^+,\kappa) -->> (\mu^+, \mu) for all regular $\kappa$, and $\mu < \kappa$, and talk about the barriers that we face when trying to extend this result.   Link to recording. zoom אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
zoom
Abstract
In this talk I will present some results regarding the consistency strength of Higher variants of Chang's Conjecture. 
I will start with the classical result by Silver of Chang's Conjecture from $\omega_1$-Erdos cardinal.  
Then, I will give an upper bound for the consistency strength of  $(\aleph_{\omega+1}, \aleph_{\omega}) -->>(\aleph_1, \aleph_0)$
and $(\aleph_4, \aleph_3) -->> (\aleph_2, \aleph_1)$ (joint with Eskew)
from supercompactness assumptions. 
If time permits, I will describe the strategy for obtaining a global result:
(\kappa^+,\kappa) -->> (\mu^+, \mu)
for all regular $\kappa$, and $\mu < \kappa$, and talk about the barriers that we face when trying to extend this result.
 
Link to recording.

Last Updated Date : 23/11/2020