Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\Sigma^{\mu}_2$ is decidable for $\Pi^{\mu}_2$   Given a $\Pi^{\mu}_2$ formula of the modal $\mu$ calculus, it is decidable
whether it is equivalent to a $\Sigma^{\mu}_2$ formula.

15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas