Cardinal sequences and cohen real extensions

István Juhász*, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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 אN0)V levels of size ω. 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.

Original languageEnglish
Pages (from-to)75-88
Number of pages14
JournalFundamenta Mathematicae
Volume181
Issue number1
DOIs
StatePublished - 2004

Keywords

  • 0-dimensional
  • Cardinal sequence
  • Cohen reals
  • Locally compact scattered space
  • Regular space
  • Superatomic Boolean algebra

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