Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact saturation in pseudo-elementary classes for simple and stable
  theories   We study PC-exact saturation for stable and simple theories. Among other
results, we show that PC-exact saturation characterizes the stability cardinals
of size at least continuum of a countable stable theory and, additionally, that
simple unstable theories have PC-exact saturation at singular cardinals,
satisfying mild set-theoretic hypotheses, which had previously been open even
for the random graph. We characterize supersimplicity of countable theories in
terms of having PC-exact saturation at singular cardinals of countable
cofinality. We also consider the local analogue of PC-exact saturation, showing
that local PC-exact saturation for singular cardinals of countable cofinality
characterizes supershort theories.

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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: dg-ga