Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Baire spaces of homogeneous structures in which Borel sets are Ramsey   We prove that for any homogeneous structure $\mathbf{K}$ in a language with
finitely many relation symbols of arity at most two satisfying SDAP$^+$, there
are natural topological spaces of subcopies of $\mathbf{K}$, forming subspaces
of the Baire space, in which all Borel sets are Ramsey. As a corollary, we
obtain an analogue of the Nash-Williams Theorem which recovers exact big Ramsey
degrees for these structures, answering a question raised by Todorcevic at the
2019 Luminy Workshop on Set Theory. Moreover, we show that the rationals and
similar homogeneous structures satisfy an analogue of the Ellentuck theorem.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th