More constructions for Boolean algebras

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish
Pages (from-to)401-441
Number of pages41
JournalArchive for Mathematical Logic
Volume41
Issue number5
DOIs
StatePublished - Jul 2002

Keywords

  • Boolean algebras
  • Cardinal invariants of Boolean algebras
  • Depth of Boolean algebra
  • Forcing
  • PCF application
  • Set theory
  • ZFC constructions

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