# Does the HOD dichotomy preclude a model of a proper class of supercompact cardinals which are not HOD-supercompact?

## Shoshana Friedman

### Kingsborough Community College, CUNY

I will be presenting my version of the notes of Woodin’s talk at the Appalachian Set Theory seminar on his paper, the HOD Dichotomy. In particular I will be discussing Woodin’s version and definition of a model of set theory being “far from HOD”. I will also be discussing how this relates to some possible future results (see title) as well as a recent result of Cheng,Friedman and Hamkins, which seem on their face to contradict Woodin’s premise.

Professor Friedman earned her Ph.D. at the CUNY Graduate Center in 2010 under the supervision of Arthur W. Apter, and now holds a faculty position at Kingsborough CC of CUNY and is active in the logic seminars at the Graduate Center. She conducts research in forcing and large cardinals, with a particular emphasis on aspects of definability.