Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The theories of Baldwin-Shi hypergraphs and their atomic models   We show that the quantifier elimination result for the Shelah-Spencer almost
sure theories of sparse random graphs $G(n,n^{-\alpha})$ given by Laskowski in
$[7]$ extends to their various analogues. The analogues will be obtained as
theories of generic structures of certain classes of finite structures with a
notion of strong substructure induced by rank functions and we will call the
generics Baldwin-Shi hypergraphs. In the process we give a method of
constructing extensions whose `relative rank' is negative but arbitrarily small
in context. We give a necessary and sufficient condition for the theory of a
Baldwin-Shi hypergraph to have atomic models. We further show that for certain
well behaved classes of theories of Baldwin-Shi hypergraphs, the existentially
closed models and the atomic models correspond.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom