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.