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WEAK DISTRIBUTIVITY IMPLYING DISTRIBUTIVITY

Published online by Cambridge University Press:  29 June 2016

DAN HATHAWAY
DAN HATHAWAY*
Affiliation:
MATHEMATICS DEPARTMENT UNIVERSITY OF DENVER DENVER, CO 80208, USA E-mail: daniel.hathaway@du.edu
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Abstract

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Let $B$ be a complete Boolean algebra. We show that if λ is an infinite cardinal and $B$ is weakly (λ ω , ω)-distributive, then $B$ is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that $B$ is weakly (2κ , κ)-distributive and $B$ is (α, 2)-distributive for each α < κ, then $B$ is (κ, 2)-distributive.

Keywords

Set Theorycomplete Boolean algebrasdistributive lawsweak distributivityweakly compact cardinalsthe tower number

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 2 , June 2016, pp. 711 - 717
Copyright
Copyright © The Association for Symbolic Logic 2016 

References

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