Diamond, square, and level by level equivalence

DOI10.1007/s00153-004-0252-0zbMath1068.03038OpenAlexW2093950082MaRDI QIDQ1777269

Arthur W. Apter

Publication date: 13 May 2005

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

Full work available at URL: https://doi.org/10.1007/s00153-004-0252-0

zbMATH Keywords

Level by level equivalence between strong compactness and supercompactnessStrongly compact cardinalSupercompact cardinalDiamondSquareStrong cardinal

Mathematics Subject Classification ID

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

Related Items (7)

IDENTITY CRISIS BETWEEN SUPERCOMPACTNESS AND VǑPENKA’S PRINCIPLE ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ Strong combinatorial principles and level by level equivalence ⋮ An \(L\)-like model containing very large cardinals ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ Group radicals and strongly compact cardinals ⋮ A universal indestructibility theorem compatible with level by level equivalence

Cites Work

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• Set theory. An introduction to independence proofs
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• SQUARES, SCALES AND STATIONARY REFLECTION
• On level by level equivalence and inequivalence between strong compactness and supercompactness
• On strong compactness and supercompactness
• How large is the first strongly compact cardinal? or a study on identity crises
• Strong axioms of infinity and elementary embeddings
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• Extensions with the approximation and cover properties have no new large cardinals
• The fine structure of the constructible hierarchy
• On the strong equality between supercompactness and strong compactness
• Identity crises and strong compactness. II: Strong cardinals
• Gap forcing

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