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
Joel David Hamkins (2000). The Lottery Preparation. Annals of Pure and Applied Logic 101 (2-3):103-146.
Joel David Hamkins (1998). Destruction or Preservation as You Like It. Annals of Pure and Applied Logic 91 (2-3):191-229.

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