Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generic expansion and Skolemization in NSOP$_1$ theories   We study expansions of NSOP$_1$ theories that preserve NSOP$_1$. We prove
that if $T$ is a model complete NSOP$_1$ theory eliminating the quantifier
$\exists^{\infty}$, then the generic expansion of $T$ by arbitrary constant,
function, and relation symbols is still NSOP$_1$. We give a detailed analysis
of the special case of the theory of the generic $L$-structure, the model
companion of the empty theory in an arbitrary language $L$. Under the same
hypotheses, we show that $T$ may be generically expanded to an NSOP$_1$ theory
with built-in Skolem functions. In order to obtain these results, we establish
strengthenings of several properties of Kim-independence in NSOP$_1$ theories,
adding instances of algebraic independence to their conclusions.

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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas