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- W308839283 abstract "Foreman (For13) proved the Duality Theorem, which gives an al- gebraic characterization of certain ideal quotients in generic extensions. As an application he proved that generic supercompactness of !1 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 application we prove that if !1 is generically strong, then it remains so after adding any number of Cohen subsets of !1; however many other !1-closed posets—such as Colp!1,!2q—can destroy the generic strength of !1. This generalizes some results of Gitik-Shelah (GS89a) about indestructibility of strong cardinals to the generically strong context. We also prove similar theorems for successor cardinals larger than !1." @default.
- W308839283 created "2016-06-24" @default.
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- W308839283 date "2016-01-01" @default.
- W308839283 modified "2023-09-27" @default.
- W308839283 title "Indestructibility of generically strong cardinals" @default.
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- W308839283 doi "https://doi.org/10.4064/fm232-2-3" @default.
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