An \(L\)-like model containing very large cardinals

DOI10.1007/s00153-008-0071-9zbMath1145.03031OpenAlexW1969203133MaRDI QIDQ937214

James Cummings, Arthur W. Apter

Publication date: 20 August 2008

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

Full work available at URL: https://doi.org/10.1007/s00153-008-0071-9

zbMATH Keywords

strongly compact cardinalsquaresupercompact cardinallevel by level equivalence between strong compactness and supercompactnessdiamond plusdiamond primeddiamond star

Mathematics Subject Classification ID

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

Related Items (4)

Subcompact cardinals, squares, and stationary reflection ⋮ Strong combinatorial principles and level by level equivalence ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ Large cardinals and locally defined well-orders of the universe

Cites Work

• Unnamed Item
• Diamond, square, and level by level equivalence
• The Souslin problem
• SQUARES, SCALES AND STATIONARY REFLECTION
• Indestructibility and the level-by-level agreement between strong compactness and supercompactness
• Precipitous ideals
• On strong compactness and supercompactness
• Strong axioms of infinity and elementary embeddings
• On the Existence of Nonregular Ultrafilters and the Cardinality of Ultrapowers
• Gap Forcing: Generalizing the Lévy-Solovay Theorem
• A very weak square principle
• 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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