More on cardinal invariants of Boolean algebras

Andrzej Roslanowski, Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B0×B1)=max{irr(B0),irr(B 1)}. We prove consistency of the statement "there is a Boolean algebra B such that irr(B)<s(BB)" and we force a superatomic Boolean algebra B* such that s(B*)=inc(B*)=κ, irr(B*)=Id(B*)=κ+ and Sub(B*)=2κ+. Next we force a superatomic algebra B0 such that irr(B0)<inc(B0) and a superatomic algebra B1 such that t(B1)>Aut(B1). Finally we show that consistently there is a Boolean algebra B of size λ such that there is no free sequence in B of length λ, there is an ultrafilter of tightness λ (so t(B)=λ) and λ∉DepthHs(B).

Original languageEnglish
Pages (from-to)1-37
Number of pages37
JournalAnnals of Pure and Applied Logic
Volume103
Issue number1-3
DOIs
StatePublished - 15 May 2000

Keywords

  • 03E10
  • 03E35
  • Boolean algebras
  • Cardinal functions
  • Forcing
  • Primary 03G05
  • Secondary 03E05

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