# Sh:974

• Garti, S., & Shelah, S. (2019). {\rm Depth}^+ and {\rm Length}^+ of Boolean Algebras. Houston Journal of Mathematics, 45(4), 953–963. 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.
• published version (11p)
Bib entry
@article{Sh:974,
author = {Garti, Shimon and Shelah, Saharon},
title = {{${\rm Depth}^+$ and ${\rm Length}^+$ of Boolean Algebras}},
journal = {Houston Journal of Mathematics},
volume = {45},
number = {4},
year = {2019},
pages = {953-963},
note = {\href{https://arxiv.org/abs/1303.3704}{arXiv: 1303.3704}},
arxiv_number = {1303.3704}
}