Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Criteria for exact saturation and singular compactness   We introduce the class of unshreddable theories, which contains the simple
and NIP theories, and prove that such theories have exactly saturated models in
singular cardinals, satisfying certain set-theoretic hypotheses. We also give
criteria for a theory to have singular compactness.

21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th