Archive for Mathematical Logic

, Volume 48, Issue 2, pp 141–157

The polarized Ramsey’s theorem



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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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

Personalised recommendations