The least strongly compact can be the least strong and indestructible

DOI10.1016/j.apal.2006.05.002zbMath1115.03073OpenAlexW2033514078MaRDI QIDQ861814

Arthur W. Apter

Publication date: 2 February 2007

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.2006.05.002

zbMATH Keywords

strongly compact cardinalindestructibilityPrikry forcingstrong cardinalRadin forcing

Mathematics Subject Classification ID

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

Related Items (5)

IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE ⋮ Indestructible strong compactness but not supercompactness ⋮ On tall cardinals and some related generalizations ⋮ Superstrong and other large cardinals are never Laver indestructible ⋮ Indestructible strong compactness and level by level inequivalence

Cites Work

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• Changing cofinalities and the nonstationary ideal
• On certain indestructibility of strong cardinals and a question of Hajnal
• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Some remarks on indestructibility and Hamkins' lottery preparation
• Measurable cardinals and the continuum hypothesis
• The lottery preparation
• Strong compactness, measurability, and the class of supercompact cardinals
• SQUARES, SCALES AND STATIONARY REFLECTION
• Strong axioms of infinity and elementary embeddings
• The least measurable can be strongly compact and indestructible
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• Small forcing creates neither strong nor Woodin cardinals
• Extensions with the approximation and cover properties have no new large cardinals
• Identity crises and strong compactness. II: Strong cardinals
• Gap forcing

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