THE TREE PROPERTY UP TO ℵω+1

被引：23

作者：

Neeman, Itay ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2014年 / 79卷 / 02期

基金：

美国国家科学基金会;

关键词：

Aronszajn trees; tree property; supercompact cardinals; ARONSZAJN TREES;

D O I：

10.1017/jsl.2013.25

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Assuming omega supercompact cardinals we force to obtain a model where the tree property holds both at aleph(omega + 1), and at N-n for all 2 <= n < omega. A model with the former was obtained by Magidor-Shelah from a large cardinal assumption above a huge cardinal, and recently by Sinapova from omega supercompact cardinals. A model with the latter was obtained by Cummings-Foreman from omega supercompact cardinals. Our model, where the two hold simultaneously, is another step toward the goal of obtaining the tree property on increasingly large intervals of successor cardinals.

引用

页码：429 / 459

页数：31

共 9 条

[1] ARONSZAJN TREES ON CHI-2 AND CHI-3 [J].

ABRAHAM, U .

ANNALS OF PURE AND APPLIED LOGIC, 1983, 24 (03) :213-230

[2] The tree property [J].

Cummings, J ;

Foreman, M .

ADVANCES IN MATHEMATICS, 1998, 133 (01) :1-32

[3] The consistency strength of successive cardinals with the tree property [J].

Foreman, M ;

Magidor, M ;

Schindler, RD .

JOURNAL OF SYMBOLIC LOGIC, 2001, 66 (04) :1837-1847

[4] The tree property at successors of singular cardinals [J].

Magidor, M ;

Shelah, S .

ARCHIVE FOR MATHEMATICAL LOGIC, 1996, 35 (5-6) :385-404

[5]

Mitchell W., 1972, Annals of Mathematical Logic, V5, P21, DOI [10.1016/0003-4843(72)90017-4, DOI 10.1016/0003-4843(72)90017-4]

[6] ARONSZAJN TREES AND FAILURE OF THE SINGULAR CARDINAL HYPOTHESIS [J].

Neeman, Itay .

JOURNAL OF MATHEMATICAL LOGIC, 2009, 9 (01) :139-157

[7]

Specker E., 1949, C MATH, V2, P9

[8] Fragility and indestructibility of the tree property [J].

Unger, Spencer .

ARCHIVE FOR MATHEMATICAL LOGIC, 2012, 51 (5-6) :635-645

[9]

UNGER SPENCER, MODEL CUMMI IN PRESS

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