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Coloring the rationals in reverse mathematics

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 نشر من قبل Ludovic Patey
 تاريخ النشر 2015
  مجال البحث
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Ramseys theorem for pairs asserts that every 2-coloring of the pairs of integers has an infinite monochromatic subset. In this paper, we study a strengthening of Ramseys theorem for pairs due to Erdos and Rado, which states that every 2-coloring of the pairs of rationals has either an infinite 0-homogeneous set or a 1-homogeneous set of order type eta, where eta is the order type of the rationals. This theorem is a natural candidate to lie strictly between the arithmetic comprehension axiom and Ramseys theorem for pairs. This Erdos-Rado theorem, like the tree theorem for pairs, belongs to a family of Ramsey-type statements whose logical strength remains a challenge.



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