### More on cardinal invariants of Boolean algebras

by Roslanowski and Shelah. [RoSh:599]

Annals Pure and Applied Logic, 2000

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 x 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)< 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
B_0 such that irr(B_0)< inc(B_0) and a superatomic algebra
B_1 such that t(B_1)> 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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