Indestructible strong compactness but not supercompactness

DOI10.1016/j.apal.2012.01.006zbMath1250.03092OpenAlexW2165294800MaRDI QIDQ435196

Grigor Sargsyan, Arthur W. Apter, M. B. Gitik

Publication date: 11 July 2012

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apal.2012.01.006

zbMATH Keywords

indestructibilityPrikry forcingstrongly compactsupercompact

Mathematics Subject Classification ID

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

Related Items (4)

Mixed Levels of Indestructibility ⋮ Fragility and indestructibility. II ⋮ Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions ⋮ Indestructible strong compactness and level by level inequivalence

Cites Work

• Unnamed Item
• Failures of SCH and level by level equivalence
• The least strongly compact can be the least strong and indestructible
• 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
• Forcing Magidor iteration over a core model below \(0^P\)
• SQUARES, SCALES AND STATIONARY REFLECTION
• How large is the first strongly compact cardinal? or a study on identity crises
• Strong axioms of infinity and elementary embeddings
• The least measurable can be strongly compact and indestructible
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• Set Theory
• Extensions with the approximation and cover properties have no new large cardinals
• Identity crises and strong compactness. II: Strong cardinals
• Gap forcing

This page was built for publication: Indestructible strong compactness but not supercompactness