Fragility and indestructibility of the tree property

被引：18

作者：

Unger, Spencer ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2012年 / 51卷 / 5-6期

关键词：

Tree property; Indestructibility; Fragility; Large cardinals; Forcing;

D O I：

10.1007/s00153-012-0287-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove various theorems about the preservation and destruction of the tree property at omega (2). Working in a model of Mitchell [9] where the tree property holds at omega (2), we prove that omega (2) still has the tree property after ccc forcing of size or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we prove from a supercompact cardinal that the tree property at omega (2) can be indestructible under omega (2)-directed closed forcing.

引用

页码：635 / 645

页数：11

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