More on cardinal invariants of Boolean algebras
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 times B1)= max(irr(B0),irr(B1)). We prove consistency of the statement ``there is a Boolean algebra B such that irr(B)<s(B otimes B)'' and we force a superatomic Boolean algebra B* such that s(B*)=inc(B*)=kappa, irr(B*)=Id(B*)=kappa+ and Sub(B*)=2(kappa+). 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 lambda such that there is no free sequence in B of length lambda, there is an ultrafilter of tightness lambda (so t(B)=lambda) and lambda notin Depth(Hs)(B).
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