Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abstract decomposition theorem and applications   Let K be an Abstract Elementary Class. Under the asusmptions that K has a
nicely behaved forking-like notion, regular types and existence of some prime
models we establish a decomposition theorem for such classes. The decomposition
implies a main gap result for the class K. The setting is general enough to
cover \aleph_0-stable first-order theories (proved by Shelah in 1982),
Excellent Classes of atomic models of a first order tehory (proved Grossberg
and Hart 1987) and the class of submodels of a large sequentially homogenuus
\aleph_0-stable model (which is new).

11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
30
The categories of this paper are: q-alg