Claims

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1974_07_01_hindman: Theorem 3.1 of Hindman's 1974 paper in J. Combin. Theory Ser. A: for every finite partition of the positive integers some cell holds all finite sums of distinct terms of some infinite sequence; refereed, credited by the site.

1974_11_01_baumgartner: Theorem 1 of Baumgartner's 1974 note in J. Combin. Theory Ser. A: when the nonnegative integers are partitioned into k sets, some set contains an infinite sequence with all its finite sums; a second refereed proof.

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