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 language | English |
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Pages (from-to) | 1-37 |
Number of pages | 37 |
Journal | Annals of Pure and Applied Logic |
Volume | 103 |
Issue number | 1-3 |
DOIs | |
State | Published - 15 May 2000 |
Keywords
- 03E10
- 03E35
- Boolean algebras
- Cardinal functions
- Forcing
- Primary 03G05
- Secondary 03E05