Indestructible strong compactness and level by level inequivalence

DOI10.1002/malq.201200067zbMath1291.03093OpenAlexW2111916375MaRDI QIDQ2856639

Arthur W. Apter

Publication date: 30 October 2013

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/malq.201200067

zbMATH Keywords

strongly compact cardinalindestructibilitylottery sumsupercompact cardinalnon-reflecting stationary set of ordinalsMahlo cardinallevel by level inequivalence between strong compactness and supercompactnessPříkrý forcingPříkrý sequence

Mathematics Subject Classification ID

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

Related Items (2)

On the consistency strength of level by level inequivalence ⋮ Precisely controlling level by level behavior

Cites Work

• Indestructible strong compactness but not supercompactness
• Failures of SCH and level by level equivalence
• The least strongly compact can be the least strong and indestructible
• 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
• The lottery preparation
• SQUARES, SCALES AND STATIONARY REFLECTION
• Indestructibility and level by level equivalence and inequivalence
• Strong axioms of infinity and elementary embeddings
• The least measurable can be strongly compact and indestructible
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• Extensions with the approximation and cover properties have no new large cardinals
• On the strong equality between supercompactness and strong compactness
• Gap forcing

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