Sh:974

• Garti, S., & Shelah, S. (2019). Depth^+ and Length^+ of Boolean algebras. Houston J. Math., 45(4), 953–963. arXiv: 1303.3704 MR: 4102862
• 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.
• Version 2017-04-30_11 (11p) published version (11p)

@article{Sh:974,
 author = {Garti, Shimon and Shelah, Saharon},
 title = {{Depth$^+$ and Length$^+$ of Boolean algebras}},
 journal = {Houston J. Math.},
 fjournal = {Houston Journal of Mathematics},
 volume = {45},
 number = {4},
 year = {2019},
 pages = {953--963},
 issn = {0362-1588},
 mrnumber = {4102862},
 mrclass = {03G05 (03C20 03E05)},
 note = {\href{https://arxiv.org/abs/1303.3704}{arXiv: 1303.3704}},
 arxiv_number = {1303.3704}
}