Restrictions of Ultrapower Embeddings from Generic Extensions to their Ground Model
Seminar
Speaker
Eyal Kaplan (TAU)
Date
20/07/2023 - 16:00 - 14:00Add to Calendar
2023-07-20 14:00:00
2023-07-20 16:00:00
Restrictions of Ultrapower Embeddings from Generic Extensions to their Ground Model
Assume that V[G] is a generic (set) forcing over the ground model V, and let \kappa be a measurable cardinal in V[G].
Let j_W \colon V[G] \to M be an ultrapower embedding associated with a normal measure W\in V[G] on \kappa.
What can be said about j_W\restriction_{V}? Is it definable in V? Is it an iterated ultrapower of V by its measures/extenders?
We will survey some known results. These results do not apply to the case where the forcing being used is an iteration of Prikry forcings.
Our main focus will be to present new tools for dealing with iterations of Prikry forcings, taken with various supports (Nonstationary support, Full support and Easton support).
This is a joint work with Moti Gitik.
Math department, Seminar room
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Math department, Seminar room
Abstract
Assume that V[G] is a generic (set) forcing over the ground model V, and let \kappa be a measurable cardinal in V[G].
Let j_W \colon V[G] \to M be an ultrapower embedding associated with a normal measure W\in V[G] on \kappa.
What can be said about j_W\restriction_{V}? Is it definable in V? Is it an iterated ultrapower of V by its measures/extenders?
We will survey some known results. These results do not apply to the case where the forcing being used is an iteration of Prikry forcings.
Our main focus will be to present new tools for dealing with iterations of Prikry forcings, taken with various supports (Nonstationary support, Full support and Easton support).
This is a joint work with Moti Gitik.
Last Updated Date : 16/07/2023
