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Failures of SCH and Level by Level Equivalence
Archive for Mathematical Logic 45 (7):831-838 (2006)
Abstract
We construct a model for the level by level equivalence between strong compactness and supercompactness in which below the least supercompact cardinal κ, there is a stationary set of cardinals on which SCH fails. In this model, the structure of the class of supercompact cardinals can be arbitrary.Other Versions
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Citations of this work
Indestructible strong compactness and level by level inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
Indestructible strong compactness but not supercompactness.Arthur W. Apter, Moti Gitik & Grigor Sargsyan - 2012 - Annals of Pure and Applied Logic 163 (9):1237-1242.
Indestructibility under adding Cohen subsets and level by level equivalence.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):271-279.
References found in this work
Strong axioms of infinity and elementary embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Squares, scales and stationary reflection.James Cummings, Matthew Foreman & Menachem Magidor - 2001 - Journal of Mathematical Logic 1 (1):35-98.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
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