Wednesday, March 25, 20155:00 pmSet theory seminarModels of PAGC 7314

# Generic I0 at $\aleph_\omega$

## Vincenzo Dimonte

### Technische Universität Wien

It is common practice to consider the generic version of large cardinals defined with an elementary embedding, but what happens when such cardinals are really large? The talk will concern a form of generic I0 and the consequences of this over-the-top hypothesis on the “largeness” of the powerset of $\aleph_\omega$. This research is a result of discussions with Hugh Woodin.

Dr. Vincenzo Dimonte is currently a post-doctoral fellow at the Technische Universität Wien. He holds a PhD from the Università di Torino, completed under the supervision of W. Hugh Woodin and Alessandro Andretta in 2010. His research interests lie in the study of very large cardinals in set theory.