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

## Andrew Brooke-Taylor

### University of Bristol

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.

Andrew Brooke-Taylor is a set theorist, who applies large cardinal axioms and other tools and techniques from set theory to other areas of mathematics, particularly category theory and algebraic topology. He received his doctorate in 2007 from the Kurt Gödel Research Center and the Universität Wien, and has held postdoctoral positions at the University of Bristol and at Kobe University.