Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric Spaces Are Universal for Bi-interpretation with Metric Structures   In the context of metric structures introduced by Ben Yaacov, Berenstein,
Henson, and Usvyatsov, we exhibit an explicit encoding of metric structures in
countable signatures as pure metric spaces in the empty signature, showing that
such structures are universal for bi-interpretation among metric structures
with positive diameter. This is analogous to the classical encoding of
arbitrary discrete structures in finite signatures as graphs, but is stronger
in certain ways and weaker in others. There are also certain fine grained
topological concerns with no analog in the discrete setting.

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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an