More on cardinal invariants of Boolean algebras Original Research Article

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 View the MathML source. We prove consistency of the statement “there is a Boolean algebra View the MathML source such that View the MathML source” and we force a superatomic Boolean algebra View the MathML source such that View the MathML source, View the MathML source and View the MathML source. Next we force a superatomic algebra View the MathML source such that View the MathML source and a superatomic algebra View the MathML source such that View the MathML source. Finally we show that consistently there is a Boolean algebra View the MathML source of size λ such that there is no free sequence in View the MathML source of length λ, there is an ultrafilter of tightness λ (so View the MathML source) and View the MathML source.