Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Monk's questions   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.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th