# Woodin’s AD-conjecture and local Reinhardt cardinals

## Scott Cramer

### Rutgers University

We will discuss Woodin’s AD-conjecture, which gives a deep relationship between very large cardinals and determined sets of reals. In particular we will show that the AD-conjecture holds for the axiom I0 and that there are many interesting consequences of this fact. We will also discuss the notion of a local Reinhardt cardinal and how variations of the AD-conjecture might show that such cardinals do not exist.

Scott Cramer received his Ph.D. from the University of California-Berkeley in 2012, with a thesis on reflection of large cardinals, written under the supervision of Hugh Woodin. He is presently a Triennial Assistant Professor at Rutgers University, working in set theory, with specific interests in very large cardinals and determinacy axioms.