# Sh:974

• Garti, S., & Shelah, S. {\rm DEPTH}^+ and {\rm LENGTH}^+ of Boolean Algebras. arXiv: 1303.3704
• Abstract:
Suppose \kappa=\textrm{cf}(\kappa), \lambda>\textrm{cf}(\lambda)=\kappa^+ and \lambda=\lambda^\kappa. We prove that there exist a sequence \langle{\mathbf{B}}_i:i<\kappa\rangle of Boolean algebras and an ultrafilter D on \kappa so that \lambda=\prod\limits_{i<\kappa} {\rm Depth}^+({\mathbf{B}}_i)/D< {\rm Depth}^+(\prod\limits_{i< \kappa}{\mathbf B}_i/D)= \lambda^+. An identical result holds also for {\rm Length}^+. The proof is carried in ZFC and it holds even above large cardinals.
@article{Sh:974,
title = {{${\rm DEPTH}^+$ and ${\rm LENGTH}^+$ of Boolean Algebras}},
}