Kurt Gödel Research Center

2018 seminar talk: Stationary reflection at $\aleph_{\omega+1}$

Talk held by Yair Hayut (Hebrew University of Jerusalem, 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.