We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several examples of colorings of the integers which do not have computable witnesses to Hindman's Theorem
Keywords Hindman's Theorem   reverse mathematics   Ramsey theory
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DOI 10.1215/00294527-1626518
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Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.

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On the Strength of Two Recurrence Theorems.Adam R. Day - 2016 - Journal of Symbolic Logic 81 (4):1357-1374.

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