Stationary Reflection and the Failure OF SCH at ${\aleph }_{{\omega }_1}$

Abstract

Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at ${\aleph }_{{\omega }_1}$, answering a question of Ben-Neria, Hayut, and Unger: We prove from the existence of uncountably many supercompact cardinals the consistency of ${\aleph }_{{\omega }_1}$ is strong limit together with $2^{{\aleph }_{{\omega }_1}}>{\aleph }_{{\omega }_1+1}$ and every stationary set of ${\aleph }_{{\omega }_1+1}$ reflects.

corrected some typos