Cardinal sequences and Cohen real extensions

István Juhász, et al. "Cardinal sequences and Cohen real extensions." Fundamenta Mathematicae 181.1 (2004): 75-88. <http://eudml.org/doc/282869>.

@article{IstvánJuhász2004,
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 $(2^\{ℵ₀\})^V$ 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.},
author = {István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy},
journal = {Fundamenta Mathematicae},
keywords = {locally compact scattered space; superatomic Boolean algebra; Cohen reals; cardinal sequences; zero-dimensional},
language = {eng},
number = {1},
pages = {75-88},
title = {Cardinal sequences and Cohen real extensions},
url = {http://eudml.org/doc/282869},
volume = {181},
year = {2004},
}

TY - JOUR
AU - István Juhász
AU - Saharon Shelah
AU - Lajos Soukup
AU - Zoltán Szentmiklóssy
TI - Cardinal sequences and Cohen real extensions
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 1
SP - 75
EP - 88
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 $(2^{ℵ₀})^V$ 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.
LA - eng
KW - locally compact scattered space; superatomic Boolean algebra; Cohen reals; cardinal sequences; zero-dimensional
UR - http://eudml.org/doc/282869
ER -