Note A Ramsey Statement for Infinite Groups


If κ is a cardinal, n < ω, then there exists an Abelian group G such that if F: Gκ, then there exist distinct elements ai,αG (1≤in,α<κ), and a color τ<κ such that if 1≤i0<···<irn, αr<κ, then \(F\left( {{a_{{i_1},{\alpha _1}}} + \cdots + {a_{{i_r},{\alpha _r}}}} \right) = \tau \).

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Correspondence to Péter Komjáth.

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Komjáth, P. Note A Ramsey Statement for Infinite Groups. Combinatorica 38, 1017–1020 (2018).

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Mathematics Subject Classification (2000)

  • 03E05
  • 05D10
  • 20F99