Force to change large cardinal strength
The CUNY Graduate Center
Suppose $kappain V$ is a cardinal with large cardinal property $A$. In this talk, I will present several theorems which exhibit a notion of forcing $mathbb P$ such that if $Gsubseteq mathbb P$ is $V$-generic, then the cardinal $kappa$ no longer has property $A$ in the forcing extension $V[G]$, but has as many large cardinal properties below $A$ as possible. I will also introduce new large cardinal notions and degrees for large cardinal properties.
This talk is the speaker’s dissertation defense.
Erin Carmody is a visiting assistant professor at Nebraska Wesleyan University. Her research is in the field of set theory. She received her doctorate in 2015 under the supervision of Joel David Hamkins.