  Monk asks (problems 13, 15 in his list; pi is the algebraic density):''For a
Boolean algebra B, aleph_0 <= theta <= pi (B), does B have a subalgebra B' with
pi (B')= theta ?'' If theta is regular the answer is easily positive, we show
that in general it may be negative, but for quite many singular cardinals - it
is positive; the theorems are quite complementary. Next we deal with pi-chi and
we show that the pi-chi of an ultraproduct of Boolean algebras is not
necessarily the ultraproduct of the pi-chi 's. We also prove that for infinite
Boolean algebras A_i (i< kappa) and a non-principal ultrafilter D on kappa : if
n_i< aleph_0 for i< kappa and mu = prod_{i< kappa} n_i/D is regular, then
pi-chi(A) >= mu. Here A= prod_{i< kappa}A_i/D. By a theorem of Peterson the
regularity of mu is needed.
