Universal indestructibility for degrees of supercompactness and strongly compact cardinals

被引：0
|
作者：
Arthur W. Apter
Grigor Sargsyan
机构：
[1] Baruch College of CUNY,Department of Mathematics
[2] The CUNY Graduate Center,Department of Mathematics
[3] University of California,Group in Logic and the Methodology of Science
来源：
Archive for Mathematical Logic | 2008年 / 47卷
关键词：
Universal indestructibility; Indestructibility; Measurable cardinal; Strongly compact cardinal; Supercompact cardinal; 03E35; 03E55;
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学科分类号：
摘要：
We establish two theorems concerning strongly compact cardinals and universal indestructibility for degrees of supercompactness. In the first theorem, we show that universal indestructibility for degrees of supercompactness in the presence of a strongly compact cardinal is consistent with the existence of a proper class of measurable cardinals. In the second theorem, we show that universal indestructibility for degrees of supercompactness is consistent in the presence of two non-supercompact strongly compact cardinals, each of which exhibits a significant amount of indestructibility for its strong compactness.
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页码：133 / 142
页数：9
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