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

 

Height and width of superatomic Boolean algebras


Author: Judy Roitman
Journal: Proc. Amer. Math. Soc. 94 (1985), 9-14
MSC: Primary 06E99; Secondary 03E35
MathSciNet review: 781045
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Abstract: Cantor-Bendixson height and width of superatomic Boolean algebras is investigated and it is shown that (1) you don't need a Canadian tree to construct an $ {\omega _1}$-thin-thick superatomic Boolean algebra;

(2) $ {\mathbf{c}}$ can be very large and for all $ \kappa < {\mathbf{c}}$ and all uncountable $ \lambda ,\kappa < {\mathbf{c}}$, there are no $ \kappa $-thin-very tall, $ \lambda $-thin-tall, $ \kappa $-very thin-thick, or $ \lambda $-thin-thick superatomic Boolean algebras on $ \kappa $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0781045-0
PII: S 0002-9939(1985)0781045-0
Article copyright: © Copyright 1985 American Mathematical Society