Katětov order on Borel ideals

被引:0
|
作者
Michael Hrušák
机构
[1] UNAM,Instituto de Matemáticas
来源
关键词
Filter; Ideal; Katětov order; Category dichotomy; Measure dichotomy; Primary and Secondary: 03E15; 03E17; 03E05; 03E35;
D O I
暂无
中图分类号
学科分类号
摘要
We study the Katětov order on Borel ideals. We prove two structural theorems (dichotomies), one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.
引用
收藏
页码:831 / 847
页数:16
相关论文
共 50 条
  • [1] Some Structural Aspects of the Katětov Order on Borel Ideals
    Osvaldo Guzmán-González
    David Meza-Alcántara
    [J]. Order, 2016, 33 : 189 - 194
  • [2] On Katětov and Katětov–Blass orders on analytic P-ideals and Borel ideals
    Hiroshi Sakai
    [J]. Archive for Mathematical Logic, 2018, 57 : 317 - 327
  • [3] Katětov order between Hindman, Ramsey and summable ideals
    Filipow, Rafal
    Kowitz, Krzysztof
    Kwela, Adam
    [J]. ARCHIVE FOR MATHEMATICAL LOGIC, 2024, 63 (7-8) : 859 - 876
  • [4] STRUCTURE OF SUMMABLE TALL IDEALS UNDER KATĚTOV ORDER
    He, Jialiang
    Li, Zuoheng
    Zhang, Shuguo
    [J]. JOURNAL OF SYMBOLIC LOGIC, 2023,
  • [5] Katetov order on Borel ideals
    Hrusak, Michael
    [J]. ARCHIVE FOR MATHEMATICAL LOGIC, 2017, 56 (7-8) : 831 - 847
  • [6] Katětov Functors
    Wiesław Kubiś
    Dragan Mašulović
    [J]. Applied Categorical Structures, 2017, 25 : 569 - 602
  • [7] THE BRUHAT ORDER ON ABELIAN IDEALS OF BOREL SUBALGEBRAS
    Gandini, Jacopo
    Maffei, Andrea
    Frajria, Pierluigi Moseneder
    Papi, Paolo
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (10) : 6999 - 7018
  • [8] Some Structural Aspects of the Kattov Order on Borel Ideals
    Guzman-Gonzalez, Osvaldo
    Meza-Alcantara, David
    [J]. ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS, 2016, 33 (02): : 189 - 194
  • [9] Borel ideals
    Marinari, AG
    [J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2001, 4B (01): : 207 - 237
  • [10] On the structure of Borel ideals in-between the ideals εD and Fin ⊗ Fin in the Katetov order
    Das, Pratulananda
    Filipow, Rafal
    Glab, Szymon
    Tryba, Jacek
    [J]. ANNALS OF PURE AND APPLIED LOGIC, 2021, 172 (08)