Yair Hayut will  continue his talks on the Gluing Property



Abstract: One of the characterizations of strongly compact cardinals is the ability to extend every $\kappa$-complete filter to a $\kappa$-complete ultrafilter. By restricting this property to different families of filters we obtain a variety of compactness principles, of varying strengths. For example, by restricting our attention to $\kappa$-complete filters on $\kappa$, we obtain the notion of $\kappa$-compactness, which is still rather strong. Restricting the filters to be normal does not reduce the strength.
In this sequence of talks, I will discuss the problem of restricting the filter extension property to filters which are obtained by trying to "glue together" $\kappa$-complete ultrafilter. As those filters are not very far from being ultrafilters already, it is expected that this property will be weaker, and it is consistently much weaker than $\kappa$-compactness. We will start by drawing some connections between strong compactness and this property. Then, we will start analysing how to get the consistency of this property from large cardinals in the level of strong cardinals. The final goal is to obtain it from a measurable cardinal of high Mitchell order.   
This is joint work with Alejandro Poveda




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


Meeting ID: 816 7272 4380Passcode: 998395