algebra universalis

, Volume 20, Issue 2, pp 135-142

First online:

Two consistency results concerning thin-tall Boolean algebras

  • Winfried JustAffiliated withWarsaw University

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In this paper we show that the following is relatively consistent withZFC +⌝CH: “There is no superatomic Boolean algebra of height ω2+1 and widthω, and there is no superatomic Boolean algebraA with\(\left| {At(A)} \right| = \omega , \omega \leqslant \left| {At^{(\alpha )} (A)} \right| \leqslant \omega _1 \) for 0<α<ω1 and\(\left| {At^{(\omega _1 )} (A)} \right| = \omega _2 \)