Set theory seminarFriday, October 25, 201310:00 am

# Killing Inaccessible Cardinals Softly

## Erin Carmody

### The CUNY Graduate Center

I shall introduce the killing-them-softly phenomenon among large cardinals by showing how it works for inaccessible and Mahlo cardinals. A large cardinal is killed softly whenever, by forcing, one of its large cardinal properties is destroyed while as many as possible weaker large cardinal properties, below this one, are preserved. I shall also explore the various degrees of inaccessibility and show Mahlo cardinals are $alpha$-hyper$^{beta}$-inaccessible and beyond.

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.

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on October 17th, 2013