Failures of SCH and Level by Level Equivalence

Archive for Mathematical Logic 45 (7):831-838 (2006)
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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

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10.1007/s00153-006-0006-2

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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.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
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 (01):35-98.
On strong compactness and supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.

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