Cardinal characteristics and strong compactness

In this talk, I presented a part of my thesis which had to do with controlling the cardinal characteristics of strongly compact cardinals. I focused on the ultrafilter number, due to the recent progress made by Brooke-Taylor, Fischer, Friedman and Montoya who showed that it is possible to fully control the value of the ultrafilter number of a supercompact cardinal. I talked about an application of this, which is that it is possible to collapse any supercompact cardinal to a non-supercompact strongly compact cardinal and still be able to fully control its ultrafilter number.

The slides can be found at the Winter School’s website, here.