On tightness and depth in superatomic Boolean algebras

Shelah, Saharon; Spinas, Otmar

doi:10.1090/S0002-9939-99-04944-8

On tightness and depth in superatomic Boolean algebras
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by Saharon Shelah and Otmar Spinas

Proc. Amer. Math. Soc. 127 (1999), 3475-3480

DOI: https://doi.org/10.1090/S0002-9939-99-04944-8

Published electronically: May 13, 1999

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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$^{+}(B)\geq \lambda ^{+}$, then depth$(B)\geq \lambda$. This improves a theorem of Dow and Monk.

References

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