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 notions
Keywords Extendible cardinals  Indestructible cardinals  Generalized continuum hypothesis (GCH)
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DOI 10.1007/s00153-013-0333-z
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References found in this work BETA

The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Laver Sequences for Extendible and Super-Almost-Huge Cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.
Fragile Measurability.Joel Hamkins - 1994 - Journal of Symbolic Logic 59 (1):262-282.

View all 9 references / Add more references

Citations of this work BETA

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.
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.
Ultrahuge cardinals.Konstantinos Tsaprounis - 2016 - Mathematical Logic Quarterly 62 (1-2):77-87.

View all 6 citations / Add more citations

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