Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: There is a Van Douwen MAD family   We prove in ZFC that there is a MAD family of functions in omega^omega which
is also maximal with respect to infinite partial functions. This solves a 20
year old question of Van Douwen. We also strengthen a result of J. Steprans
stating that strongly MAD families of functions cannot be analytic. We show
that analytic MAD families of functions, if they exist, must satisfy some
strong constraints.

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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci