Cofinalities of Borel ideals

被引：5
|
作者：
Hrusak, Michael [1 ,2 ]
Rojas-Rebolledo, Diego [3 ]
Zapletal, Jindrich [2 ,4 ]
机构：
[1] Univ Nacl Autonoma Mexico, Ctr Ciencias Matemat, Morelia 58089, Michoacan, Mexico
[2] Acad Sci Czech Republic, Inst Math, CR-11567 Prague 1, Czech Republic
[3] St Marys Univ, Dept Math & Comp Sci, Halifax, NS B3H 3C3, Canada
[4] Univ Florida, Dept Math, Gainesville, FL 32611 USA
来源：
MATHEMATICAL LOGIC QUARTERLY | 2014年 / 60卷 / 1-2期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1002/malq.201200079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the possible values of the cofinality invariant for various Borel ideals on the natural numbers. We introduce the notions of a fragmented and gradually fragmented F sigma ideal and prove a dichotomy for fragmented ideals. We show that every gradually fragmented ideal has cofinality consistently strictly smaller than the cardinal invariant b and produce a model where there are uncountably many pairwise distinct cofinalities of gradually fragmented ideals.
引用
收藏
页码：31 / 39
页数：9
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