Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elementary chains and compact spaces with a small diagonal   It is a well known open problem if, in ZFC, each compact space with a small
diagonal is metrizable. We explore properties of compact spaces with a small
diagonal using elementary chains of submodels. We prove that ccc subspaces of
such spaces have countable \pi-weight. We generalize a result of Gruenhage
about spaces which are metrizably fibered. Finally we discover that if there is
a Luzin set of reals, then every compact space with a small diagonal will have
many points of countable character.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs