Algebra Seminar talk
2026-10-23
Jiaming Zhang
Maximal Prikry Sequence of K
Abstract:
We investigate the covering machinery of the Jensen–Steel core model $K$ under the hypothesis that there is no inner model with a Woodin cardinal. Mitchell and Schimmerling showed that if $\nu>\omega_2$ is regular in $K$ but singular in $V$, then $\nu$ is measurable in $K$. Under additional hypotheses, we obtain a maximal Prikry sequence $C$ for a measure on $\nu$ in $K$. In a more restrictive setting, we prove that every subset of $\nu$ of size less than $|\nu|$ is covered by a set in $K[C]$ of size less than $|\nu|$. We will focus on the core model arguments behind these results and discuss their optimality from the work of Benhamou–Schimmerling. The talk is based primarily on my PhD thesis, completed at Carnegie Mellon University under the supervision of Ernest Schimmerling.