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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.

References [Enhancements On Off] (What's this?)

  • [1] K. Bozeman, Ph.D. thesis, University of North Texas, 1990.
  • [2] M. Burke, Weakly dense subsets of the measure algebra, Proc. Amer. Math. Soc. 106 (1989), 867-874. MR 961402 (89m:28011)
  • [3] W. Just, unpublished manuscript.
  • [4] S. Koppelberg, General theory of Boolean algebras: handbook of Boolean algebras, North-Holland, Amsterdam, 1989. MR 991609

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Keywords: Dense, weakly dense, homogeneously weakly dense, nowhere relatively dense, cellularity
Article copyright: © Copyright 1991 American Mathematical Society

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