Archive for Mathematical Logic

, Volume 48, Issue 2, pp 141–157

The polarized Ramsey’s theorem


DOI: 10.1007/s00153-008-0108-0

Cite this article as:
Dzhafarov, D.D. & Hirst, J.L. Arch. Math. Logic (2009) 48: 141. doi:10.1007/s00153-008-0108-0


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)


Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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