Indestructibility and the level-by-level agreement between strong compactness and supercompactness

Journal of Symbolic Logic 67 (2):820-840 (2002)
Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can
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DOI 10.2178/jsl/1190150111
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References found in this work BETA
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Destruction or Preservation as You Like It.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.
Identity Crises and Strong Compactness.Arthur W. Apter & James Cummings - 2001 - Archive for Mathematical Logic 40 (1):25-38.

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Citations of this work BETA
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
The Failure of GCH at a Degree of Supercompactness.Brent Cody - 2012 - Mathematical Logic Quarterly 58 (1):83-94.
Indestructibility, HOD, and the Ground Axiom.Arthur W. Apter - 2011 - Mathematical Logic Quarterly 57 (3):261-265.

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