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  1. On the indestructibility aspects of identity crisis.Grigor Sargsyan - 2009 - Archive for Mathematical Logic 48 (6):493-513.
    We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi–Magidor theorem from (in The independence between the concepts of compactness and supercompactness, circulated manuscript), i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact cardinals can be the first n measurable cardinals while the strong (...)
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  • Woodin for strong compactness cardinals.Stamatis Dimopoulos - 2019 - Journal of Symbolic Logic 84 (1):301-319.
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  • Universal indestructibility for degrees of supercompactness and strongly compact cardinals.Arthur W. Apter & Grigor Sargsyan - 2008 - Archive for Mathematical Logic 47 (2):133-142.
    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 (...)
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