More on cardinal invariants of Boolean algebras

Andrzej Roslanowski; Saharon Shelah

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More on cardinal invariants of Boolean algebras

Andrzej Roslanowski·Saharon Shelah

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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(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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BibTeX RIS

Andrzej Roslanowski, Saharon Shelah. 1998-08-12. More on cardinal invariants of Boolean algebras. https://arxiv.org/abs/math/9808056

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