On tightness and depth in superatomic Boolean algebras

DOI10.1090/S0002-9939-99-04944-8zbMATH Open0939.06013arXivmath/9802135MaRDI QIDQ4268901

Saharon Shelah, Otmar Spinas

Publication date: 28 October 1999

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Abstract: We introduce a large cardinal property which is consistent with L and show that for every superatomic Boolean algebra B and every cardinal lambda with the large cardinal property, if tightness^+(B) >= lambda^+, then depth (B) >= lambda. This improves a theorem of Dow and Monk.

Full work available at URL: https://arxiv.org/abs/math/9802135

zbMATH Keywords

tightnessdepthsuperatomic Boolean algebraslarge cardinal property

Mathematics Subject Classification ID

Consistency and independence results (03E35) Large cardinals (03E55) Structure theory of Boolean algebras (06E05)

Related Items (6)

Remarks on superatomic Boolean algebras ⋮ A Consistency Result on Thin-Tall Superatomic Boolean Algebras ⋮ Unnamed Item ⋮ On Depth and \(\text{Depth}^{+}\) of Boolean algebras ⋮ Erratum to ``Depth, \(\pi\)-character, and tightness in superatomic Boolean algebras ⋮ The depth of ultraproducts of Boolean algebras

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