一个小的超滤数在每一个单一的基数

Pub Date : 2023-10-31 DOI:10.1007/s10474-023-01377-9

T. Benhamou, S. Jirattikansakul

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引用次数: 0

摘要

我们在\(\aleph_{\omega_1}\)上得到一个小的超滤数。此外，我们还开发了一种具有崩塌的重叠强扩展力的版本，该版本可以保持顶部基数\(\kappa\)不可接近。我们应用这一强迫构造了一个模型，其中\(\kappa\)是最难接近的，\( V_\kappa \)是正则点处的GCH模型，奇异点处的SCH失效，所有奇异点处的超滤数都很小。

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A small ultrafilter number at every singular cardinal

We obtain a small ultrafilter number at \(\aleph_{\omega_1}\). Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal \(\kappa\) inaccessible. We apply this forcing to construct a model where \(\kappa\) is the least inaccessible and \( V_\kappa \) is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small.

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