On the strong equality between supercompactness and strong compactness
On the strong equality between supercompactness and strong compactness
复制标题
论超紧性与强紧性的强等式
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
S. Shelah
中科院分区：
文献类型：
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作者：
Arthur W. Apter;S. Shelah
我们证明了超紧性和强紧性即使作为正则基对的性质也是等价的。Speciflcally,我们表明,如果V j = ZFC +我们给定的模型(有趣的情况下包含supercompactness实例),还有一些红衣主教和coflnality保留通用扩展V (G) j = ZFC +我们,(a)(保护- tion)••,定期,如果V j =•,超紧”,V (G) j =•,超紧”所以,(b)(等价)••,定期、V (G) j =•强烈紧凑”如果V (G) j =•,超紧”,除非它可能是基数的可测量极限，它们是超紧凑的。
We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Speciflcally, we show that if V j= ZFC + GCH is a given model (which in interesting cases contains instances of supercompactness), then there is some cardinal and coflnality preserving generic extension V (G)j= ZFC + GCH in which, (a) (preserva- tion) for •• ‚ regular, if V j= • is ‚ supercompact", then V (G)j= • is ‚ supercompact" and so that, (b) (equivalence) for •• ‚ regular, V (G)j= • is ‚ strongly compact" ifi V (G)j= • is ‚ supercompact", except possibly ifis a measurable limit of cardinals which are ‚ supercompact.