Cardinal sequences and cohen real extensions

István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy

doi:10.4064/fm181-1-3

Cardinal sequences and cohen real extensions

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

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	75-88
Number of pages	14
Journal	Fundamenta Mathematicae
Volume	181
Issue number	1
DOIs	https://doi.org/10.4064/fm181-1-3
State	Published - 2004

Keywords

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

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AU - Shelah, Saharon

AU - Soukup, Lajos

AU - Szentmiklóssy, Zoltán

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Y1 - 2004

N2 - 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.

AB - 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.

KW - 0-dimensional

KW - Cardinal sequence

KW - Cohen reals

KW - Locally compact scattered space

KW - Regular space

KW - Superatomic Boolean algebra

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Cardinal sequences and cohen real extensions

Abstract

Keywords

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