Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transfinite Approximation of Hindman's Theorem   Hindman's Theorem states that in any finite coloring of the integers, there
is an infinite set all of whose finite sums belong to the same color. This is
much stronger than the corresponding finite form, stating that in any finite
coloring of the integers there are arbitrarily long finite sets with the same
property. We extend the finite form of Hindman's Theorem to a "transfinite"
version for each countable ordinal, and show that Hindman's Theorem is
equivalent to the appropriate transfinite approximation holding for every
countable ordinal. We then give a proof of Hindman's Theorem by directly
proving these transfinite approximations.

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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph