**November 6**

**Ernest Schimmerling**,
Carnegie Mellon University

**Covering at limit cardinals of K**

Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let $\nu$ be a singular ordinal such that $\nu > \omega_2$ and $\mathrm{cf}(\nu) < | \nu |$. Suppose $\nu$ is a regular cardinal in K. Then $\nu$ is a measurable cardinal in K. Moreover, if $\mathrm{cf}(\nu) > \omega$, then $o^\mathrm{K}(\nu) \ge \mathrm{cf}(\nu)$.

I will say something intuitive and wildly incomplete but not misleading about the meaning of the theorem, how it is proved, and the history of results behind it.