Cardinal sequences and Cohen real extensions

Tom 181 / 2004

István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy Fundamenta Mathematicae 181 (2004), 75-88 MSC: 54A25, 06E05, 54G12, 03E35. DOI: 10.4064/fm181-1-3

Streszczenie

We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most $(2^{\aleph_0})^V$ levels of size $\omega$. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of $0$-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.

Autorzy

  • István JuhászAlfréd Rényi Institute of Mathematics
    Reáltanoda u. 13–15
    H-1053 Budapest, Hungary
    e-mail
  • Saharon ShelahInstitute of Mathematics
    The Hebrew University of Jerusalem
    91904 Jerusalem, Israel
    e-mail
  • Lajos SoukupAlfréd Rényi Institute of Mathematics
    Reáltanoda u. 13–15
    H-1053 Budapest, Hungary
    e-mail
  • Zoltán SzentmiklóssyDepartment of Analysis
    Eötvös Loránd University
    Pázmány Péter sétány 1/c
    H-1117 Budapest, Hungary
    e-mail

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