Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The small index property for homogeneous models in AECs   We prove a version of a small index property theorem for strong amalgamation
classes. Our result builds on an earlier theorem by Lascar and Shelah (in their
case, for saturated models of uncountable first-order theories). We then study
versions of the small index property for various non-elementary classes. In
particular, we obtain the small index property for quasiminimal pregeometry
structures.

9
The categories of this paper are: nlin
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The categories of this paper are: econ
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio