# Generic I0 at $\aleph_\omega$
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 extravagant hypothesis on the "largeness" of the powerset of $\aleph_\omega$. This research is a result of discussions with Hugh Woodin.