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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the relationship between density and weak density in Boolean algebras


Author: Kyle Bozeman
Journal: Proc. Amer. Math. Soc. 112 (1991), 1137-1141
MSC: Primary 06E05
MathSciNet review: 1049841
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Abstract: Given a homogeneous, complete Boolean algebra $ B$, it is shown that $ {\text{d}}(B) \leq \min ({2^{ < {\text{wd}}(B)}},\sup \{ {\lambda ^{c(B)}}:\lambda < {\text{wd}}(B)\} )$ in ZFC, where $ d(B)$ is the density, $ {\text{wd}}(B)$ is the weak density, and $ c(B)$ is the cellularity of $ B$. A corollary to this result is that $ d(B) = {\text{wd}}(B)$ in ZFC+GCH.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1049841-5
PII: S 0002-9939(1991)1049841-5
Keywords: Dense, weakly dense, homogeneously weakly dense, nowhere relatively dense, cellularity
Article copyright: © Copyright 1991 American Mathematical Society