On extendible cardinals and the GCH

被引：7
|
作者：
Tsaprounis, Konstantinos [1 ]
机构：
[1] Univ Barcelona, Dept Log Hist & Philosophy Sci, Barcelona 08001, Spain
来源：
ARCHIVE FOR MATHEMATICAL LOGIC | 2013年 / 52卷 / 5-6期
关键词：
Extendible cardinals; Indestructible cardinals; Generalized continuum hypothesis (GCH);
D O I：
10.1007/s00153-013-0333-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a characterization of extendibility in terms of embeddings between the structures H.. 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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页码：593 / 602
页数：10
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