The lottery preparation
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Publication:1964017
DOI10.1016/S0168-0072(99)00010-XzbMath0949.03045arXivmath/9808012WikidataQ56813202 ScholiaQ56813202MaRDI QIDQ1964017
Publication date: 3 December 2000
Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/9808012
Related Items (56)
Identity crises and strong compactness. III: Woodin cardinals ⋮ Indestructibility properties of Ramsey and Ramsey-like cardinals ⋮ Coding into HOD via normal measures with some applications ⋮ 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 ⋮ Diamond (on the regulars) can fail at any strongly unfoldable cardinal ⋮ On extendible cardinals and the GCH ⋮ Unnamed Item ⋮ Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness ⋮ Strongly uplifting cardinals and the boldface resurrection axioms ⋮ On supercompactness and the continuum function ⋮ Inner-model reflection principles ⋮ Inner models with large cardinal features usually obtained by forcing ⋮ Absoluteness via resurrection ⋮ Indestructibility of Vopěnka's principle ⋮ Indestructible strong compactness but not supercompactness ⋮ Resurrection axioms and uplifting cardinals ⋮ 2007 European Summer Meeting of the Association for Symbolic Logic: Logic Colloquium '07 ⋮ Hierarchies of forcing axioms I ⋮ NORMAL MEASURES ON A TALL CARDINAL ⋮ On some properties of Shelah cardinals ⋮ A Laver-like indestructibility for hypermeasurable cardinals ⋮ The consistency of level by level equivalence with $V = {\rm HOD}$, the Ground Axiom, and instances of square and diamond ⋮ Large cardinals need not be large in HOD ⋮ Local saturation of the non-stationary ideal over \(\mathcal P_{\kappa}\lambda\) ⋮ The least weakly compact cardinal can be unfoldable, weakly measurable and nearly \(\theta\)-supercompact ⋮ HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES ⋮ Universal indestructibility for degrees of supercompactness and strongly compact cardinals ⋮ Characterizations of the weakly compact ideal on \(P_\kappa\lambda\) ⋮ Indestructibility, instances of strong compactness, and level by level inequivalence ⋮ An equiconsistency for universal indestructibility ⋮ Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions ⋮ JOINT DIAMONDS AND LAVER DIAMONDS ⋮ The weakly compact reflection principle need not imply a high order of weak compactness ⋮ Indestructibility and destructible measurable cardinals ⋮ Superstrong and other large cardinals are never Laver indestructible ⋮ Laver and set theory ⋮ Set-theoretic geology ⋮ The tree property at the \(\aleph_{2 n}\)'s and the failure of SCH at \(\aleph_\omega\) ⋮ Strongly compact cardinals and the continuum function ⋮ The proper and semi-proper forcing axioms for forcing notions that preserve ℵ₂ or ℵ₃ ⋮ Large cardinals and definable well-orders on the universe ⋮ Indestructibility and stationary reflection ⋮ Indestructibility under adding Cohen subsets and level by level equivalence ⋮ On spaces with $\sigma$-closed-discrete dense sets ⋮ The failure of GCH at a degree of supercompactness ⋮ Strongly unfoldable cardinals made indestructible ⋮ Tall cardinals ⋮ Indestructible strong compactness and level by level inequivalence ⋮ A universal indestructibility theorem compatible with level by level equivalence ⋮ Large cardinals with few measures ⋮ Indestructibility and the level-by-level agreement between strong compactness and supercompactness ⋮ Blowing up the power set of the least measurable ⋮ MORE ON THE PRESERVATION OF LARGE CARDINALS UNDER CLASS FORCING
Cites Work
- On certain indestructibility of strong cardinals and a question of Hajnal
- Making the supercompactness of \(\nu\) indestructible under \(\nu\)-directed closed forcing
- Destruction or preservation as you like it
- Patterns of compact cardinals
- The wholeness axiom and Laver sequences
- On strong compactness and supercompactness
- How large is the first strongly compact cardinal? or a study on identity crises
- The least measurable can be strongly compact and indestructible
- Fragile measurability
- Canonical seeds and Prikry trees
- Laver indestructibility and the class of compact cardinals
- Laver sequences for extendible and super-almost-huge cardinals
- Boolean extensions and measurable cardinals
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