Indestructibility of generically strong cardinals
نویسندگان
چکیده
منابع مشابه
Indestructibility of Generically Strong Cardinals
Foreman [For13] proved the Duality Theorem, which gives an algebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of ω1 is preserved by any proper forcing. We generalize portions of Foreman’s Duality Theorem to the context of generic extender embeddings and ideal extenders (as introduced by Claverie [Cla10]). As an ...
متن کاملIndestructibility properties of remarkable cardinals
Remarkable cardinals were introduced by Schindler, who showed that the existence of a remarkable cardinal is equiconsistent with the assertion that the theory of L(R) is absolute for proper forcing [Sch00]. Here, we study the indestructibility properties of remarkable cardinals. We show that if κ is remarkable, then there is a forcing extension in which the remarkability of κ becomes indestruct...
متن کاملIndestructibility and destructible measurable cardinals
Say that κ’s measurability is destructible if there exists a <κ-closed forcing adding a new subset of κ which destroys κ’s measurability. For any δ, let λδ =df The least beth fixed point above δ. Suppose that κ is indestructibly supercompact and there is a measurable cardinal λ > κ. It then follows that A1 = {δ < κ | δ is measurable, δ is not a limit of measurable cardinals, δ is not δ+ strongl...
متن کاملA Note on Indestructibility and Strong Compactness
If κ < λ are such that κ is both supercompact and indestructible under κ-directed closed forcing which is also (κ+,∞)-distributive and λ is 2λ supercompact, then by [3, Theorem 5], {δ < κ | δ is δ+ strongly compact yet δ isn’t δ+ supercompact} must be unbounded in κ. We show that the large cardinal hypothesis on λ is necessary by constructing a model containing a supercompact cardinal κ in whic...
متن کاملSingular cardinals and strong extenders
We investigate the circumstances under which there exist a singular cardinal μ and a short (κ, μ)-extender E witnessing “κ is μ-strong”, such that μ is singular in Ult(V,E).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2016
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm232-2-3