Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixed quantifier prefixes over Diophantine equations with integer
  variables   In this paper we study mixed quantifier prefixes over Diophantine equations
with integer variables. For example, we prove that $\forall^2\exists^4$ over
$\mathbb Z$ is undecidable, that is, there is no algorithm to determine for any
$P(x_1,\ldots,x_6)\in\mathbb Z[x_1,\ldots,x_6]$ whether $$\forall x_1\forall
x_2\exists x_3\exists x_4\exists x_5\exists x_6(P(x_1,\ldots,x_6)=0),$$ where
$x_1,\ldots,x_6$ are integer variables. We also have some similar undecidable
results with universal quantifies bounded, for example,
$\exists^2\forall^2\exists^2$ over $\mathbb Z$ with $\forall$ bounded is
undecidable. We conjecture that $\forall^2\exists^2$ over $\mathbb Z$ is
undecidable.

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The categories of this paper are: mtrl-th
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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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: acc-phys
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ