On extendible cardinals and the GCH

On extendible cardinals and the GCH

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)...

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Veröffentlicht in:Archive for mathematical logic 2013-08, Vol.52 (5-6), p.593-602
1. Verfasser: Tsaprounis, Konstantinos
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Archives
Embedded structures
Logic
Mathematical analysis
Mathematical logic
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Preserving
Set theory
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Zusammenfassung: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.
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-013-0333-z