Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Which Classes of Structures Are Both Pseudo-elementary and Definable by
  an Infinitary Sentence?   When classes of structures are not first-order definable, we might still try
to find a nice description. There are two common ways for doing this. One is to
expand the language, leading to notions of pseudo-elementary classes, and the
other is to allow infinite conjuncts and disjuncts. In this paper we examine
the intersection. Namely, we address the question: Which classes of structures
are both pseudo-elementary and $\mathcal{L}_{\omega_1 \omega}$-elementary? We
find that these are exactly the classes that can be defined by an infinitary
formula that has no infinitary disjunctions.

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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex