Cardinal sequences and Cohen real extensions
逻辑
2007-05-23 v1 一般拓扑
摘要
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.
引用
@article{arxiv.math/0404322,
title = {Cardinal sequences and Cohen real extensions},
author = {István Juhász and Saharon Shelah and Lajos Soukup and Zoltán Szentmiklóssy},
journal= {arXiv preprint arXiv:math/0404322},
year = {2007}
}