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# Higher Chang Conjecture

Seminar
Speaker
Yait Hayut (HUJI)
Date
04/11/2020 - 16:00 - 14:00
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.