title: More constructions for Boolean algebras
abstract: 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)/sup kappa /<|B| implies ind(B)>/sup kappa /V Depth(B)>or=log(|B|)
keyphrases: Boolean algebras prescribed behaviour free product ZFC ultraproducts homomorphic images cardinal invariants