Shelah, Saharon More constructions for Boolean algebras. (English) Zbl 1023.03043 Arch. Math. Logic 41, No. 5, 401-441 (2002). Summary: We construct Boolean algebras with prescribed behaviour concerning depth for the free product of two Boolean algebras over a third, in ZFC using pcf; assuming squares we get results on ultraproducts. We also deal with the family of cardinalities and topological density of homomorphic images of Boolean algebras (you can translate it to topology – on the cardinalities of closed subspaces); and lastly we deal with inequalities between cardinal invariants, mainly \(d(B)^\kappa < |B|\Rightarrow \text{ind}(B) > \kappa \vee \text{Depth}(B) \geq {\log}(|B|)\). MSC: 03E04 Ordered sets and their cofinalities; pcf theory 06E05 Structure theory of Boolean algebras 03E35 Consistency and independence results Keywords:Boolean algebras; depth; free product; ultraproducts; cardinal invariants; ZFC constructions; pcf application; forcing PDFBibTeX XMLCite \textit{S. Shelah}, Arch. Math. Logic 41, No. 5, 401--441 (2002; Zbl 1023.03043) Full Text: DOI arXiv