More on cardinal invariants of Boolean algebras

Details More on cardinal invariants of Boolean algebras More on cardinal invariants of Boolean algebras

1998-08-12

arxiv.org/abs/math/9808056v1

Mathematics

Logic

accepted for Annals of Pure and Applied Logic

Scientific paper

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(B_0 times B_1)= max(irr(B_0),irr(B_1)). We prove consistency of the statement ``there is a Boolean algebra B such that irr(B)Aut(B_1). 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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