Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Winning the pressing down game but not Banach Mazur   Let $S$ be the set of those $\alpha\in\omega_2$ that have cofinality
$\omega_1$. It is consistent relative to a measurable that the nonempty player
wins the pressing down game of length $\omega_1$, but not the Banach Mazur game
of length $\omega+1$ (both games starting with $S$).

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The categories of this paper are: hep-th
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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: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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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: q-bio
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th