Archive for Mathematical Logic

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

Effectiveness for infinite variable words and the Dual Ramsey Theorem

  • Joseph S. Miller
  • Reed Solomon


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 ACA 0 over RCA 0 . We show that neither VW(2,2) nor OVW(2,2) is provable in WKL 0 . These results give partial answers to questions posed by Friedman and Simpson [3].


Partial Answer Variable Word Effective Mathematic Open Coloring Combinatorial Principle 
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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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