A Model in Which GCH Holds at Successors but Fails at Limits
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Publication:3991810
DOI10.2307/2154075zbMath0758.03022OpenAlexW4248749797MaRDI QIDQ3991810
Publication date: 28 June 1992
Full work available at URL: https://doi.org/10.2307/2154075
GCHcontinuum functiongeneric extensionsuccessor cardinalRadin forcingcardinal collapsinghypermeasurable cardinalsingular cardinals problemreverse Easton extensions
Consistency and independence results (03E35) Large cardinals (03E55) Continuum hypothesis and Martin's axiom (03E50)
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Exactly controlling the non-supercompact strongly compact cardinals ⋮ Strong ultrapowers and long core models ⋮ Extender-based Radin forcing ⋮ On the indestructibility aspects of identity crisis ⋮ Precalibre pairs of measure algebras ⋮ INDESTRUCTIBILITY WHEN THE FIRST TWO MEASURABLE CARDINALS ARE STRONGLY COMPACT ⋮ Two-cardinal diamond star ⋮ Easton's theorem in the presence of Woodin cardinals ⋮ Possible values for \(2^{\aleph_n}\) and \(2^{\aleph_\omega}\) ⋮ On the consistency strength of level by level inequivalence ⋮ The nonstationary ideal on \(P_\kappa (\lambda )\) for \(\lambda \) singular ⋮ Negating the Galvin property ⋮ Global singularization and the failure of SCH ⋮ Easton collapses and a strongly saturated filter ⋮ Menas’ Result is Best Possible ⋮ Elementary chains and \(C ^{(n)}\)-cardinals ⋮ Capturing sets of ordinals by normal ultrapowers ⋮ When \(P_\kappa(\lambda)\) (vaguely) resembles \(\kappa\) ⋮ On the strong equality between supercompactness and strong compactness ⋮ Easton's theorem and large cardinals ⋮ Erratum for “On the consistency of local and global versions of Chang’s Conjecture” ⋮ A Laver-like indestructibility for hypermeasurable cardinals ⋮ The tree property at $\aleph _{\omega +2}$ with a finite gap ⋮ Some new upper bounds in consistency strength for certain choiceless large cardinal patterns ⋮ Universal indestructibility for degrees of supercompactness and strongly compact cardinals ⋮ The cardinality of compact spaces satisfying the countable chain condition ⋮ Power function on stationary classes ⋮ Indestructibility, instances of strong compactness, and level by level inequivalence ⋮ Indiscernible sequences for extenders, and the singular cardinal hypothesis ⋮ Game ideals ⋮ Local saturation and square everywhere ⋮ Tallness and level by level equivalence and inequivalence ⋮ Adding a lot of Cohen reals by adding a few. I ⋮ Tall cardinals ⋮ STATIONARY REFLECTION ⋮ Changing cardinal characteristics without changing \(\omega\)-sequences or cofinalities ⋮ (Weak) diamond can fail at the least inaccessible cardinal
Cites Work
- Set theory. An introduction to independence proofs
- Proper forcing
- On the singular cardinals problem. II
- Sets constructed from sequences of measures: Revisited
- The core model for sequences of measures. I
- Adding closed cofinal sequences to large cardinals
- Powers of regular cardinals
- On sequences generic in the sense of Prikry
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