# Yair Hayut: Stationary reflection at $\aleph_{\omega+1}$

Talk held by Yair Hayut (Tel-Aviv University, Israel)
at the KGRC seminar on 2018-05-17.

Abstract: Stationary reflection is one of the basic prototypes of reflection phenomena,
and its failure is related to many counterexamples for compactness
properties (such as almost free non-free abelian groups,
and more). In 1982, Magidor showed that it is consistent, relative to infinitely many
supercomapct cardinals, that stationary reflections holds at $\aleph_{\omega + 1}$.
In this talk I’m going to present a new method for forcing stationary reflection
at $\aleph_{\omega+1}$, which allows to significantly reduce the upper bound for the consistency strength of the full stationary reflection at $\aleph_{\omega+1}$ (below a single partially supercompact cardinal).

This is a joint work with Spencer Unger.