Open Access
2011 Depth of Boolean Algebras
Shimon Garti, Saharon Shelah
Notre Dame J. Formal Logic 52(3): 307-314 (2011). DOI: 10.1215/00294527-1435474


Suppose $D$ is an ultrafilter on $\kappa$ and $\lambda^\kappa = \lambda$. We prove that if ${\bf B}_i$ is a Boolean algebra for every $i < \kappa$ and $\lambda$ bounds the depth of every ${\bf B}_i$, then the depth of the ultraproduct of the ${\bf B}_i$'s mod $D$ is bounded by $\lambda^+$. We also show that for singular cardinals with small cofinality, there is no gap at all. This gives a partial answer to a previous problem raised by Monk.


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Shimon Garti. Saharon Shelah. "Depth of Boolean Algebras." Notre Dame J. Formal Logic 52 (3) 307 - 314, 2011.


Published: 2011
First available in Project Euclid: 28 July 2011

zbMATH: 1141.06010
MathSciNet: MR2822491
Digital Object Identifier: 10.1215/00294527-1435474

Primary: 03G05 , 06E05
Secondary: 03E45

Keywords: Boolean algebras , constructibility , depth

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 3 • 2011
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