Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residue field domination in real closed valued fields   We define a notion of residue field domination for valued fields which
generalizes stable domination in algebraically closed valued fields. We prove
that a real closed valued field is dominated by the sorts internal to the
residue field, over the value group, both in the pure field sort and in the
geometric sorts. These results characterize forking and \th-forking in real
closed valued fields (and also algebraically closed valued fields). We lay some
groundwork for extending these results to a power-bounded $T$-convex theory.

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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th