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)k < |B| ⇒ ind(B) > κ ∨ Depth(B) ≥ log(|B|).
Original language | English |
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Pages (from-to) | 401-441 |
Number of pages | 41 |
Journal | Archive for Mathematical Logic |
Volume | 41 |
Issue number | 5 |
DOIs | |
State | Published - Jul 2002 |
Keywords
- Boolean algebras
- Cardinal invariants of Boolean algebras
- Depth of Boolean algebra
- Forcing
- PCF application
- Set theory
- ZFC constructions