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.

引用

页码：1281 / 1290

页数：10

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