A small ultrafilter number at smaller cardinals

被引：2
|
作者：
Raghavan, Dilip [1 ]
Shelah, Saharon [2 ]
机构：
[1] Natl Univ Singapore, Dept Math, Singapore 119076, Singapore
[2] Hebrew Univ Jerusalem, Inst Math, IL-9190401 Jerusalem, Israel
来源：
ARCHIVE FOR MATHEMATICAL LOGIC | 2020年 / 59卷 / 3-4期
基金：
美国国家科学基金会; 欧盟地平线“2020”;
关键词：
Cardinal invariant; Uniform ultrafilter; Indecomposable ultrafilter; Large cardinal;
D O I：
10.1007/s00153-019-00693-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a supercompact cardinal that there is a uniform ultrafilter on aleph omega+1 which is generated by fewer than 2 aleph omega+1sets.
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页码：325 / 334
页数：10
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