Universal indestructibility for degrees of supercompactness and strongly compact cardinals

Arthur W. Apter; Grigor Sargsyan

doi:10.1007/s00153-008-0072-8

Universal indestructibility for degrees of supercompactness and strongly compact cardinals

Arthur W. Apter, Grigor Sargsyan

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	133-142
Number of pages	10
Journal	Archive for Mathematical Logic
Volume	47
Issue number	2
DOIs	https://doi.org/10.1007/s00153-008-0072-8
State	Published - Jul 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Philosophy
Logic

Keywords

Indestructibility
Measurable cardinal
Strongly compact cardinal
Supercompact cardinal
Universal indestructibility

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10.1007/s00153-008-0072-8

Cite this

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title = "Universal indestructibility for degrees of supercompactness and strongly compact cardinals",

abstract = "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.",

keywords = "Indestructibility, Measurable cardinal, Strongly compact cardinal, Supercompact cardinal, Universal indestructibility",

author = "Apter, {Arthur W.} and Grigor Sargsyan",

note = "Funding Information: The first author{\textquoteright}s research was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive grants. The first author wishes to thank James Cummings for helpful discussions on the subject matter of this paper. In addition, both authors wish to thank the referee, for many helpful comments and suggestions which were incorporated into the current version of the paper.",

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doi = "10.1007/s00153-008-0072-8",

language = "English (US)",

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T1 - Universal indestructibility for degrees of supercompactness and strongly compact cardinals

AU - Apter, Arthur W.

AU - Sargsyan, Grigor

N1 - Funding Information: The first author’s research was partially supported by PSC-CUNY grants and CUNY Collaborative Incentive grants. The first author wishes to thank James Cummings for helpful discussions on the subject matter of this paper. In addition, both authors wish to thank the referee, for many helpful comments and suggestions which were incorporated into the current version of the paper.

PY - 2008/7

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N2 - 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.

AB - 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.

KW - Indestructibility

KW - Measurable cardinal

KW - Strongly compact cardinal

KW - Supercompact cardinal

KW - Universal indestructibility

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Universal indestructibility for degrees of supercompactness and strongly compact cardinals

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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