Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fra\"iss\'e structures and a conjecture of Furstenberg   We study problems concerning the Samuel compactification of the automorphism
group of a countable first-order structure. A key motivating question is a
problem of Furstenberg and a counter-conjecture by Pestov regarding the
difference between $S(G)$, the Samuel compactification, and $E(M(G))$, the
enveloping semigroup of the universal minimal flow. We resolve Furstenberg's
problem for several automorphism groups and give a detailed study in the case
of $G = S_\infty$, leading us to define and investigate several new types of
ultrafilter on a countable set.

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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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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: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg