Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Models of expansions of N with no end extensions   We deal with models of Peano arithmetic (specifically with a question of Ali
Enayat). The methods are from creature forcing. We find an expansion of N such
that its theory has models with no (elementary) end extensions. In fact there
is a Borel uncountable set of subsets of N such that expanding N by any
uncountably many of them suffice. Also we find arithmetically closed A with no
definably closed ultrafilter on it.

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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: econ