Cardinal sequences and Cohen real extensions
Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 75-88
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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
$(2^{\aleph_0})^V$
levels of size $\omega$.
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.
Keywords:
number cohen reals ground model generic extension locally compact scattered space has aleph levels size omega complete zfc characterization cardinal sequences regular scattered spaces although classes regular dimensional scattered spaces different prove have cardinal sequences
Affiliations des auteurs :
István Juhász 1 ; Saharon Shelah 2 ; Lajos Soukup 1 ; Zoltán Szentmiklóssy 3
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author = {Istv\'an Juh\'asz and Saharon Shelah and Lajos Soukup and Zolt\'an Szentmikl\'ossy},
title = {Cardinal sequences and {Cohen} real extensions},
journal = {Fundamenta Mathematicae},
pages = {75--88},
publisher = {mathdoc},
volume = {181},
number = {1},
year = {2004},
doi = {10.4064/fm181-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm181-1-3/}
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%0 Journal Article %A István Juhász %A Saharon Shelah %A Lajos Soukup %A Zoltán Szentmiklóssy %T Cardinal sequences and Cohen real extensions %J Fundamenta Mathematicae %D 2004 %P 75-88 %V 181 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/fm181-1-3/ %R 10.4064/fm181-1-3 %G en %F 10_4064_fm181_1_3
István Juhász; Saharon Shelah; Lajos Soukup; Zoltán Szentmiklóssy. Cardinal sequences and Cohen real extensions. Fundamenta Mathematicae, Tome 181 (2004) no. 1, pp. 75-88. doi: 10.4064/fm181-1-3
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