Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Amenable colorings   Let $\kappa$ be any regular cardinal. Assuming the existence of a huge
cardinal above $\kappa$, we prove the consistency of
$\binom{\kappa^{++}}{\kappa^+}\rightarrow\binom{\tau}{\kappa^+}$ for every
ordinal $\tau<\kappa^{++}$. Likewise, we prove a full amenable relation for
$(\aleph_2,\aleph_1)$ with respect to collections which are strongly closed
under countable intersections.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th