Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions

DOI10.4064/ba8014-12-2015zbMath1336.03053OpenAlexW2185983788MaRDI QIDQ2787103

Arthur W. Apter

Publication date: 24 February 2016

Published in: Bulletin Polish Acad. Sci. Math. (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f1888c02a572457267920a7462efdd905f846ec4

zbMATH Keywords

strongly compact cardinalindestructibilitysupercompact cardinallevel by level equivalence between strong compactness and supercompactnessgitik iterationmagidor iteration of prikry forcing

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55)

Cites Work

• Indestructible strong compactness but not supercompactness
• Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness
• Changing cofinalities and the nonstationary ideal
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Measurable cardinals and the continuum hypothesis
• The lottery preparation
• Identity crises and strong compactness
• Indestructibility and the level-by-level agreement between strong compactness and supercompactness
• Indestructibility under adding Cohen subsets and level by level equivalence
• On strong compactness and supercompactness
• How large is the first strongly compact cardinal? or a study on identity crises
• The least measurable can be strongly compact and indestructible
• Singular Failures of GCH and Level by Level Equivalence
• Strong compactness and other cardinal sins
• On the strong equality between supercompactness and strong compactness
• Identity crises and strong compactness. II: Strong cardinals

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