Journal of Symbolic Logic 67 (2):820-840 (2002)

Authors
Joel David Hamkins
Oxford University
Abstract
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.
On Strong Compactness and Supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Destruction or Preservation as You Like It.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.

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Citations of this work BETA

Indestructibility and Stationary Reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.

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