Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set theoretical analogues of the Barwise-Schlipf theorem   We characterize nonstandard models of ZF (of arbitrary cardinality) that can
be expanded to Goedel-Bernays class theory plus $\Delta^1_1$-Comprehension. We
also characterize countable nonstandard models of ZFC that can be expanded to
Goedel-Bernays class theory plus $\Sigma^1_1$-Choice.

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
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
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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: dg-ga
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ