Gap Forcing: Generalizing the Lévy-Solovay Theorem

DOI10.2307/421092zbMath0933.03067arXivmath/9901108OpenAlexW2036178876MaRDI QIDQ4262606

Joel David Hamkins

Publication date: 29 March 2000

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9901108

zbMATH Keywords

large cardinalsgap forcinggeneralization of Lévy-Solovay theorem

Mathematics Subject Classification ID

Large cardinals (03E55) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (35)

Identity crises and strong compactness. III: Woodin cardinals ⋮ Coding into HOD via normal measures with some applications ⋮ Accessing the switchboard via set forcing ⋮ Mixed Levels of Indestructibility ⋮ Failures of SCH and level by level equivalence ⋮ INDESTRUCTIBILITY WHEN THE FIRST TWO MEASURABLE CARDINALS ARE STRONGLY COMPACT ⋮ The least strongly compact can be the least strong and indestructible ⋮ Unnamed Item ⋮ On the consistency strength of level by level inequivalence ⋮ Precisely controlling level by level behavior ⋮ Some structural results concerning supercompact cardinals ⋮ A remark on the tree property in a choiceless context ⋮ Indestructible strong compactness but not supercompactness ⋮ Strong combinatorial principles and level by level equivalence ⋮ More on HOD-supercompactness ⋮ 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 ⋮ Indestructibility and measurable cardinals with few and many measures ⋮ Universal indestructibility for degrees of supercompactness and strongly compact cardinals ⋮ Supercompactness and measurable limits of strong cardinals ⋮ Unfoldable cardinals and the GCH ⋮ Inaccessible cardinals, failures of GCH, and level-by-level equivalence ⋮ Indestructibility, instances of strong compactness, and level by level inequivalence ⋮ Diamond, square, and level by level equivalence ⋮ An equiconsistency for universal indestructibility ⋮ Gap forcing ⋮ Normal measures and strongly compact cardinals ⋮ Indestructibility and destructible measurable cardinals ⋮ Superstrong and other large cardinals are never Laver indestructible ⋮ Large cardinals and definable well-orders on the universe ⋮ Indestructibility and stationary reflection ⋮ Tallness and level by level equivalence and inequivalence ⋮ Indestructibility, measurability, and degrees of supercompactness ⋮ Indestructible strong compactness and level by level inequivalence ⋮ A universal indestructibility theorem compatible with level by level equivalence

Cites Work

• Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
• Destruction or preservation as you like it
• Measurable cardinals and the continuum hypothesis

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