1Department of Mathematics University of Nebraska at Omaha Omaha, NE 68182-0243, U.S.A Mathematical Institute Wrocław University 50384 Wroclaw, Poland 2Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel Department of Mathematics Rutgers University New Brunswick, NJ 08854, U.S.A.
Colloquium Mathematicum, Tome 89 (2001) no. 1, pp. 99-115
We show that, consistently, for some regular cardinals
$\theta \lambda $, there exists a Boolean algebra ${\mathbb
B}$ such that $|{\mathbb
B}|=\lambda ^+$ and for every subalgebra ${\mathbb
B}'\subseteq {\mathbb B}$ of size $\lambda ^+$ we
have $\mathop {\rm Depth}\nolimits ({\mathbb
B}')= \theta $.
Keywords:
consistently regular cardinals theta lambda there exists boolean algebra mathbb mathbb lambda every subalgebra mathbb subseteq mathbb size lambda have mathop depth nolimits mathbb theta
Affiliations des auteurs :
Andrzej Rosłanowski
1
;
Saharon Shelah
2
1
Department of Mathematics University of Nebraska at Omaha Omaha, NE 68182-0243, U.S.A Mathematical Institute Wrocław University 50384 Wroclaw, Poland
2
Institute of Mathematics The Hebrew University of Jerusalem 91904 Jerusalem, Israel Department of Mathematics Rutgers University New Brunswick, NJ 08854, U.S.A.
@article{10_4064_cm89_1_7,
author = {Andrzej Ros{\l}anowski and Saharon Shelah},
title = {Historic forcing for {Depth}},
journal = {Colloquium Mathematicum},
pages = {99--115},
year = {2001},
volume = {89},
number = {1},
doi = {10.4064/cm89-1-7},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm89-1-7/}
}
TY - JOUR
AU - Andrzej Rosłanowski
AU - Saharon Shelah
TI - Historic forcing for Depth
JO - Colloquium Mathematicum
PY - 2001
SP - 99
EP - 115
VL - 89
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm89-1-7/
DO - 10.4064/cm89-1-7
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