KUREPA TREES AND NAMBA FORCING

被引：4
|
作者：
Koenig, Bernhard [1 ]
Yoshinobu, Yasuo [1 ]
机构：
[1] Nagoya Univ, Grad Sch Informat Sci, Chikusa Ku, Nagoya, Aichi 4648601, Japan
来源：
JOURNAL OF SYMBOLIC LOGIC | 2012年 / 77卷 / 04期
关键词：
Kurepa trees; compact cardinals; Martin's Maximum; MARTINS MAXIMUM;
D O I：
10.2178/jsl.7704130
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that strongly compact cardinals and MM are sensitive to lambda-closed foreings for arbitrarily large lambda. This is done by adding 'regressive' lambda-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an omega(2)-closed poset that is not forcing equivalent to any omega(2)-directed-closed poset.
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页码：1281 / 1290
页数：10
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