# Blog Archives

# Topic Archive: supercompact cardinals

# Dissertation Defense: Force to change large cardinals

This will be the dissertation defense of the speaker. There will be a one-hour presentation, followed by questions posed by the dissertation committee, and afterwards including some questions posed by the general audience. The dissertation committee consists of Joel David Hamkins (supervisor), Gunter Fuchs, Arthur Apter, Roman Kossak and Philipp Rothmaler.

# A nice model for cardinal characteristics at a supercompact *κ*

In a throw-away comment in a relatively recent preprint, Garti and Shelah state that using the technique of Dzamonja and Shelah, one can start with a model of set theory containing a supercompact cardinal *κ*, and force to obtain a model in which *κ* remains supercompact, * 2^{κ}* is large, but the ultrafilter number at

*κ*is only

*κ*. I will present this construction, and with it further results from joint work with Vera Fischer and Diana Montoya pinning down many other generalized cardinal characteristics at

^{+}*κ*in the resulting model.