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arXiv · 2411.09048

Stationary Reflection and the Failure OF SCH at $\aleph_{\omega_1}$

Tom Benhamou·Dima Sinapova
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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.

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Tom Benhamou, Dima Sinapova. 2024-11-13. Stationary Reflection and the Failure OF SCH at $\aleph_{\omega_1}$. https://arxiv.org/abs/2411.09048

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