Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dependence and Isolated Extensions   In this paper, we show that \phi is a dependent formula if and only if all
\phi-types have an extension to a \phi-isolated \phi-type that is an
"elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we
show that the domain of this extension adds at most 2 times the independence
dimension of \phi new elements to the domain of the original \phi-type. We give
corollaries to this theorem and discuss parallels to the stable setting.

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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat