November 12
Tom Benhamou, Tel Aviv University
Intermediate Prikry-type models, quotients, and the Galvin property: Part II

We classify intermediate models of Magidor-Radin generic extensions. It turns out that similar to Gitik Kanovei and Koepke's result, every such intermediate model is of the form $V[C]$ where $C$ is a subsequence of the generic club added by the forcing. The proof uses the Galvin property for normal filters to prove that quotients of some Prikry-type forcings are $\kappa^+$-c.c. in the generic extension and therefore do not add fresh subsets to $\kappa^+$. If time permits, we will also present results regarding intermediate models of the Tree-Prikry forcing.