Mathematical Logic Quarterly 56 (1):4-12 (2010)

Abstract
We construct two models containing exactly one supercompact cardinal in which all non-supercompact measurable cardinals are strictly taller than they are either strongly compact or supercompact. In the first of these models, level by level equivalence between strong compactness and supercompactness holds. In the other, level by level inequivalence between strong compactness and supercompactness holds. Each universe has only one strongly compact cardinal and contains relatively few large cardinals
Keywords tall cardinal  Supercompact cardinal  superstrong cardinal  strong cardinal  level by level equivalence between strong compactness and supercompactness  level by level inequivalence between strong compactness and supercompactness  strongly compact cardinal
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DOI 10.1002/malq.200810039
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References found in this work BETA

Strong Axioms of Infinity and Elementary Embeddings.Robert M. Solovay - 1978 - Annals of Mathematical Logic 13 (1):73.
Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.

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Citations of this work BETA

On the Consistency Strength of Level by Level Inequivalence.Arthur W. Apter - 2017 - Archive for Mathematical Logic 56 (7-8):715-723.
Level by Level Inequivalence Beyond Measurability.Arthur W. Apter - 2011 - Archive for Mathematical Logic 50 (7-8):707-712.
More on HOD-Supercompactness.Arthur W. Apter, Shoshana Friedman & Gunter Fuchs - 2021 - Annals of Pure and Applied Logic 172 (3):102901.
Precisely Controlling Level by Level Behavior.Arthur W. Apter - 2017 - Mathematical Logic Quarterly 63 (1-2):77-84.

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