Height and width of superatomic Boolean algebras

Roitman, Judy

doi:10.1090/S0002-9939-1985-0781045-0

Height and width of superatomic Boolean algebras
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by Judy Roitman

Proc. Amer. Math. Soc. 94 (1985), 9-14

DOI: https://doi.org/10.1090/S0002-9939-1985-0781045-0

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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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