Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree spectra of analytic complete equivalence relations   We study the bi-embeddability and elementary bi-embeddability relation on
graphs under Borel reducibility and investigate the degree spectra realized by
this relations. We first give a Borel reduction from embeddability on graphs to
elementary embeddability on graphs. As a consequence we obtain that elementary
bi-embeddability on graphs is a analytic complete equivalence relation. We then
investigate the algorithmic properties of this reduction to show that every
bi-embeddability spectrum of a graph is the jump spectrum of an elementary
bi-embeddability spectrum of a graph.

10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int