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

Published online by Cambridge University Press:  12 March 2014

Arthur W. Apter  and
Joel David Hamkins
Arthur W. Apter
Affiliation:
Department of Mathematics, Baruch College of the City University of New York, New York, NY 10010, USA, E-mail: awabb@cunyvm.cuny.edu, URL: http://math.baruch.cuny.edu/~apter
Joel David Hamkins
Affiliation:
Department of Mathematics, The College of Staten Island of the City University of New York, 2800 Victory Boulevard, Staten Island, New York 10314. USA The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016. USA Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, USA, E-mail: jdh@hamkins.org, URL: http://jdh.hamkins.org
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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.

Keywords

Supercompact cardinalstrongly compact cardinalindestructibilitylevel-by-level agreement
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 820 - 840
Copyright
Copyright © Association for Symbolic Logic 2002

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