Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness
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Publication:877253
DOI10.1007/s00153-007-0034-6zbMath1110.03038OpenAlexW2046543615MaRDI QIDQ877253
Publication date: 19 April 2007
Published in: Archive for Mathematical Logic (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00153-007-0034-6
Prikry forcingGitik iterationIndestructibilityLevel by level equivalence between strong compactness and supercompactnessNon-reflecting stationary set of ordinalsStrongly compact cardinalSupercompact cardinal
Related Items (5)
Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions ⋮ Indestructibility under adding Cohen subsets and level by level equivalence ⋮ Indestructibility and level by level equivalence and inequivalence ⋮ Indestructible strong compactness and level by level inequivalence ⋮ A universal indestructibility theorem compatible with level by level equivalence
Cites Work
- 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
- Patterns of compact cardinals
- Measurable cardinals and the continuum hypothesis
- The lottery preparation
- Identity crises and strong compactness
- Supercompactness and measurable limits of strong cardinals
- Indestructibility and the level-by-level agreement between 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
- The least measurable can be strongly compact and indestructible
- Strong compactness and other cardinal sins
- On the strong equality between supercompactness and strong compactness
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