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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Tsaprounis, K. On extendible cardinals and the GCH. Arch. Math. Logic 52, 593–602 (2013). https://doi.org/10.1007/s00153-013-0333-z
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DOI: https://doi.org/10.1007/s00153-013-0333-z