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On tightness and depth in superatomic Boolean algebras
Authors:Saharon Shelah   Otmar Spinas
Affiliation:Institute of Mathematics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel ; Mathematik, ETH-Zentrum, 8092 Zürich, Switzerland
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.

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