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- W2012106622 abstract "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 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." @default.
- W2012106622 created "2016-06-24" @default.
- W2012106622 creator A5047471753 @default.
- W2012106622 creator A5085162361 @default.
- W2012106622 date "2010-01-07" @default.
- W2012106622 modified "2023-09-27" @default.
- W2012106622 title "Transfinite Approximation of Hindman's Theorem" @default.
- W2012106622 cites W1996285409 @default.
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