Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $\Sigma_2$ theory of $\mathscr{D}_h(\leq_h \mathcal{O})$ as an
  uppersemilattice with least and greatest element is decidable   We establish the decidability of the $\Sigma_2$ theory of
$\mathscr{D}_h(\leq_h \mathcal{O})$, the hyperarithmetic degrees below Kleene's
$\mathcal{O}$, in the language of uppersemilattices with least and greatest
element. This requires a new kind of initial-segment result and a new extension
of embeddings result both in the hyperarithmetic setting.

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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-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
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: econ