Title: Chang's Conjecture (joint with Monroe Eskew)

Abstract:

I will review some consistency results related to Chang's Conjecture (CC).

First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems.

Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously.

We will aim to show the consistency of the statement: (\mu^+,\mu) -->> (

u^+,

u) for all regular \mu and all

u < \mu, starting from a huge cardinal. In order to prove this we will start with the easier task in which $\mu$ is assumed to be regular. In order to get the stronger result, we will force with Radin forcing over a model in which many instances of CC hold.

Abstract:

I will review some consistency results related to Chang's Conjecture (CC).

First I will discuss some classical results of deriving instances of CC from huge cardinals and the new results for getting instances of CC from supercompact cardinals, and present some open problems.

Then, I will review the consistency proof of some versions of the Global Chang's Conjecture - which is the consistency of the occurrence many instances of CC simultaneously.

We will aim to show the consistency of the statement: (\mu^+,\mu) -->> (

u^+,

u) for all regular \mu and all

u < \mu, starting from a huge cardinal. In order to prove this we will start with the easier task in which $\mu$ is assumed to be regular. In order to get the stronger result, we will force with Radin forcing over a model in which many instances of CC hold.

## Date:

Wed, 21/11/2018 - 14:00 to 15:30

## Location:

Ross 63