Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On certain infinite extensions of the rationals with Northcott property   A set of algebraic numbers has the Northcott property if each of its subsets
of bounded Weil height is finite. Northcott's Theorem, which has many
Diophantine applications, states that sets of bounded degree have the Northcott
property. Bombieri, Dvornicich and Zannier raised the problem of finding fields
of infinite degree with this property. Bombieri and Zannier have shown that
$\IQ_{ab}^{(d)}$, the maximal abelian subfield of the field generated by all
algebraic numbers of degree at most $d$, is such a field. In this note we give
a simple criterion for the Northcott property and, as an application, we deduce
several new examples, e.g.
$\IQ(2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...)$ has the Northcott
property if and only if
$2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...$ tends to infinity.

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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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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: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex