Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dp-finite fields VI: the dp-finite Shelah conjecture   We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a
dp-finite field, then K admits a non-trivial definable henselian valuation
ring, unless K is finite, real closed, or algebraically closed. As a
consequence, the conjectural classification of dp-finite fields holds.
Additionally, dp-finite valued fields are henselian. Lastly, if K is an
unstable dp-finite expansion of a field, then K admits a unique definable
V-topology.

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The categories of this paper are: gr-qc
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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: eess
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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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: plasm-ph
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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: econ
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The categories of this paper are: q-alg