document: More constructions for Boolean algebras 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 -LRB- you can translate it to topology-on the cardinalities of closed subspaces -RRB- ; and lastly we deal with inequalities between cardinal invariants , mainly d -LRB- B -RRB- / sup kappa / < | B | implies ind -LRB- B -RRB- > / sup kappa / V Depth -LRB- B -RRB- > or = log -LRB- | B | -RRB-
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