Usuba’s Principle Can Fail at Singular Cardinals

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Journal of Symbolic Logic 89 (1):195-203 (2024)
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Abstract

We answer a question of Usuba by showing that the combinatorial principle $\mathrm {UB}_\lambda $ can fail at a singular cardinal. Furthermore, $\lambda $ can be taken to be $\aleph _\omega.$

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10.1017/jsl.2023.61

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New combinatorial principle on singular cardinals and normal ideals.Toshimichi Usuba - 2018 - Mathematical Logic Quarterly 64 (4-5):395-408.
Magidor–Malitz reflection.Yair Hayut - 2017 - Archive for Mathematical Logic 56 (3-4):253-272.

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