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Some structural results concerning supercompact cardinals
Journal of Symbolic Logic 66 (4):1919-1927 (2001)
Abstract
We show how the forcing of [5] can be iterated so as to get a model containing supercompact cardinals in which every measurable cardinal δ is δ + supercompact. We then apply this iteration to prove three additional theorems concerning the structure of the class of supercompact cardinals.Other Versions
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Citations of this work
Failure of GCH and the level by level equivalence between strong compactness and supercompactness.Arthur W. Apter - 2003 - Mathematical Logic Quarterly 49 (6):587.
Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence.Arthur W. Apter - 2006 - Mathematical Logic Quarterly 52 (5):457-463.
Failures of SCH and Level by Level Equivalence.Arthur W. Apter - 2006 - Archive for Mathematical Logic 45 (7):831-838.
An Easton theorem for level by level equivalence.Arthur W. Apter - 2005 - Mathematical Logic Quarterly 51 (3):247-253.
Indestructibility, measurability, and degrees of supercompactness.Arthur W. Apter - 2012 - Mathematical Logic Quarterly 58 (1):75-82.
References found in this work
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
How large is the first strongly compact cardinal? or a study on identity crises.Menachem Magidor - 1976 - Annals of Mathematical Logic 10 (1):33-57.
Gap forcing: Generalizing the lévy-Solovay theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Destruction or preservation as you like it.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.
Patterns of compact cardinals.Arthur W. Apter - 1997 - Annals of Pure and Applied Logic 89 (2-3):101-115.
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