A small ultrafilter number at every singular cardinal

IF 0.6 3区数学 Q3 MATHEMATICS

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

T. Benhamou, S. Jirattikansakul

引用次数: 0

Abstract

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.

查看原文本刊更多论文

一个小的超滤数在每一个单一的基数

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.