Geodesic
Historic forcing for Depth
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.
Colloquium Mathematicum, Tome 89 (2001) no. 1, pp. 99-115 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $.
DOI : 10.4064/cm89-1-7
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

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. 
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Andrzej Rosłanowski; Saharon Shelah. Historic forcing for  Depth. Colloquium Mathematicum, Tome 89 (2001) no. 1, pp. 99-115. doi: 10.4064/cm89-1-7

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