Stationary reflection for $\aleph_{\omega_1+1}$

Dima Sinapova (Rutgers U)

Jun 25. 2024, 09:15 — 10:00

In recent years there has been a lot of progress in combining stationary reflection at the successor of a singular and the failure of SCH. The motivation goes back to two classical results of Magidor: tationary reflection at $\aleph_{\omega+1}$ can be force from large cardinals; and from large cardinals, one can get the failure of SCH at $\aleph_\omega$. In this talk we will focus on the case when the singular cardinal has uncountable cofinality. We will show that from supercompact  cardinals, there is a Prikry type iteration, such that in the final model we have stationary reflection at $\aleph_{\omega+1}$ together with the failure of SCH at $\aleph_{\omega_1}$. This is joint work with Tom Benhamou.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Determinacy, Inner Models and Forcing Axioms (Workshop)
Organizer(s):
Sandra Müller (TU Vienna)
Grigor Sargsyan (Polish Academy of Science, Warsaw)
Ralf Schindler (WWU Münster)
John Steel (UC, Berkeley)