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On extendible cardinals and the GCH
Archive for Mathematical Logic 52 (5-6):593-602 (2013)
Abstract
We give a characterization of extendibility in terms of embeddings between the structures H λ . By that means, we show that the GCH can be forced (by a class forcing) while preserving extendible cardinals. As a corollary, we argue that such cardinals cannot in general be made indestructible by (set) forcing, under a wide variety of forcing notionsMy notes
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Citations of this work
Large cardinals need not be large in HOD.Yong Cheng, Sy-David Friedman & Joel David Hamkins - 2015 - Annals of Pure and Applied Logic 166 (11):1186-1198.
Elementary chains and C (n)-cardinals.Konstantinos Tsaprounis - 2014 - Archive for Mathematical Logic 53 (1-2):89-118.
On c-extendible cardinals.Konstantinos Tsaprounis - 2018 - Journal of Symbolic Logic 83 (3):1112-1131.
More on the Preservation of Large Cardinals Under Class Forcing.Joan Bagaria & Alejandro Poveda - 2023 - Journal of Symbolic Logic 88 (1):290-323.
References found in this work
The lottery preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Homogeneous iteration and measure one covering relative to HOD.Natasha Dobrinen & Sy-David Friedman - 2008 - Archive for Mathematical Logic 47 (7-8):711-718.
Laver sequences for extendible and super-almost-huge cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.
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