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
相关论文
共 50 条
  • [1] Different cofinalities of tree ideals
    Shelah, Saharon
    Spinas, Otmar
    ANNALS OF PURE AND APPLIED LOGIC, 2023, 174 (08)
  • [2] COFINALITIES OF MARCZEWSKI-LIKE IDEALS
    Brendle, Jorg
    Khomskii, Yurii
    Wohofsky, Wolfgang
    COLLOQUIUM MATHEMATICUM, 2017, 150 (02) : 269 - 279
  • [3] Borel ideals
    Marinari, AG
    BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2001, 4B (01): : 207 - 237
  • [4] FRECHET BOREL IDEALS WITH BOREL ORTHOGONAL
    Guevara, Francisco
    Uzcategui, Carlos
    COLLOQUIUM MATHEMATICUM, 2018, 152 (01) : 141 - 163
  • [5] Principal Borel ideals and Gotzmann ideals
    V. Bonanzinga
    Archiv der Mathematik, 2003, 81 : 385 - 396
  • [6] Principal Borel ideals and Gotzmann ideals
    Bonanzinga, V
    ARCHIV DER MATHEMATIK, 2003, 81 (04) : 385 - 396
  • [7] INVARIANT IDEALS AND BOREL SETS
    PELC, A
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 97 (03) : 503 - 506
  • [8] A characterization of stable and Borel ideals
    Maria Grazia Marinari
    Luciana Ramella
    Applicable Algebra in Engineering, Communication and Computing, 2005, 16 : 45 - 68
  • [9] Comparison game on Borel ideals
    Hrusak, Michael
    Meza-Alcantara, David
    COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2011, 52 (02): : 191 - 204
  • [10] Katetov order on Borel ideals
    Hrusak, Michael
    ARCHIVE FOR MATHEMATICAL LOGIC, 2017, 56 (7-8) : 831 - 847
12345