# Killing measurable and supercompact cardinals softly

## Erin Carmody

### The CUNY Graduate Center

This talk follows the theme of killing-them-softly between set-theoretic universes. The main theorems in this theme show how to force to reduce the large cardinal strength of a cardinal to a specified desired degree, for a variety of large cardinals including inaccessible, Mahlo, measurable and supercompact. The killing-them-softly theme is about both forcing and the gradations in large cardinal strength. This talk will focus on measurable and supercompact cardinals, and follows the larger theme of exploring interactions between large cardinals and forcing which is central to modern set theory.

Erin Carmody is a visiting assistant professor at Nebraska Wesleyan University. Her research is in the field of set theory. She received her doctorate in 2015 under the supervision of Joel David Hamkins.