On extendible cardinals and the GCH

Archive for Mathematical Logic 52 (5-6):593-602 (2013)
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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

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10.1007/s00153-013-0333-z

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Citations of this work

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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.
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Elementary chains and C (n)-cardinals.Konstantinos Tsaprounis - 2014 - Archive for Mathematical Logic 53 (1-2):89-118.
Ultrahuge cardinals.Konstantinos Tsaprounis - 2016 - Mathematical Logic Quarterly 62 (1-2):77-87.

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References found in this work

The lottery preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Fragile measurability.Joel Hamkins - 1994 - Journal of Symbolic Logic 59 (1):262-282.
Laver sequences for extendible and super-almost-huge cardinals.Paul Corazza - 1999 - Journal of Symbolic Logic 64 (3):963-983.

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