Archive for Mathematical Logic

, Volume 48, Issue 2, pp 141–157

The polarized Ramsey’s theorem

Article

Abstract

We study the effective and proof-theoretic content of the polarized Ramsey’s theorem, a variant of Ramsey’s theorem obtained by relaxing the definition of homogeneous set. Our investigation yields a new characterization of Ramsey’s theorem in all exponents, and produces several combinatorial principles which, modulo bounding for \({\Sigma^0_2}\) formulas, lie (possibly not strictly) between Ramsey’s theorem for pairs and the stable Ramsey’s theorem for pairs.

Mathematics Subject Classification (2000)

03B30 03F35 03D80 05D10 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.University of ChicagoChicagoUSA
  2. 2.Appalachian State UniversityBooneUSA

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