Archive for Mathematical Logic

, Volume 43, Issue 4, pp 543–555 | Cite as

Effectiveness for infinite variable words and the Dual Ramsey Theorem



We examine the Dual Ramsey Theorem and two related combinatorial principles VW(k,l) and OVW(k,l) from the perspectives of reverse mathematics and effective mathematics. We give a statement of the Dual Ramsey Theorem for open colorings in second order arithmetic and formalize work of Carlson and Simpson [1] to show that this statement implies ACA0 over RCA0. We show that neither VW(2,2) nor OVW(2,2) is provable in WKL0. These results give partial answers to questions posed by Friedman and Simpson [3].


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityUSA
  2. 2.Department of MathematicsUniversity of Connecticut StorrsUSA

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