Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $T$-convex $T$-differential fields and their immediate extensions   Let $T$ be a polynomially bounded o-minimal theory extending the theory of
real closed ordered fields. Let $K$ be a model of $T$ equipped with a
$T$-convex valuation ring and a $T$-derivation. If this derivation is
continuous with respect to the valuation topology, then we call $K$ a
$T$-convex $T$-differential field. We show that every $T$-convex
$T$-differential field has an immediate strict $T$-convex $T$-differential
field extension which is spherically complete. In some important cases, the
assumption of polynomial boundedness can be relaxed to power boundedness.

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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat