Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Erd\H{o}s-Selfridge and the Schinzel-Tijdeman theorems hold in
  $PA^-$   We show that "The product of consecutive integers is never a power" and
several results by Schinzel and Tijdeman on the solutions of the equation
$y^m=P(x)$, for $m>1$, $y>1$, and $P(x)$ a polynomial with rational
coefficients and with at least two distinct zeros, hold in a weak fragment of
Peano Arithmetic, $PA^-$, which lacks any kind of induction, and whose models
are the positive cones of discretely ordered rings.

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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph