# 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} }