# Sh:765

• Juhász, I., Shelah, S., Soukup, L., & Szentmiklóssy, Z. (2004). Cardinal sequences and Cohen real extensions. Fund. Math., 181(1), 75–88.
• 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^{\aleph_0})^V many levels of size \omega. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of the regular and of the 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.
• Version 2003-07-14_11 (14p) published version (14p)
Bib entry
@article{Sh:765,
author = {Juh{\'a}sz, Istv{\'a}n and Shelah, Saharon and Soukup, Lajos and Szentmikl{\'o}ssy, Zolt{\'a}n},
title = {{Cardinal sequences and Cohen real extensions}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {181},
number = {1},
year = {2004},
pages = {75--88},
issn = {0016-2736},
mrnumber = {2071695},
mrclass = {54A25 (03E35 06E15 54A35 54D45 54G12)},
doi = {10.4064/fm181-1-3},
note = {\href{https://arxiv.org/abs/math/0404322}{arXiv: math/0404322}},
arxiv_number = {math/0404322}
}