Joint work with Alejandro Poveda and Dima Sinapova.
Abstract. We prove the consistency of the failure of the singular cardinals hypothesis at $\aleph_\omega$ together with the reflection of all stationary subsets of $\aleph_{\omega+1}$. This shows that two classical results of Magidor (from 1977 and 1982) can hold simultaneously.
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Submitted to Advances in Mathematics, October 2021.
Accepted, October 2023.