Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of countable subdirect powers of unary algebras   A finite unary algebra $(A,F)$ has only countably many countable subdirect
powers if and only if every operation $f\in F$ is either a permutation or a
constant mapping.

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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: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol