Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let ν be a singular ordinal such that ν > ω₂ and cf(ν) < | ν |. Suppose ν is a regular cardinal in K. Then ν is a measurable cardinal in K. Moreover, if cf(ν) > ω, then o^K(ν) ≥ cf(ν).

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.