Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Turing degree spectra of differentially closed fields   The degree spectrum of a countable structure is the set of all Turing degrees
of presentations of that structure. We show that every nonlow Turing degree
lies in the spectrum of some differentially closed field (of characteristic 0,
with a single derivation) whose spectrum does not contain the computable degree
0. Indeed, this is an equivalence, for we also show that every such field of
low degree is isomorphic to a computable differential field. Relativizing the
latter result and applying a theorem of Montalban, Soskova, and Soskov, we
conclude that the spectra of countable differentially closed fields of
characteristic 0 are exactly the jump-preimages of spectra of automorphically
nontrivial countable graphs.

10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: q-fin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat