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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
Article

Abstract.

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].

Keywords

Partial Answer Variable Word Effective Mathematic Open Coloring Combinatorial Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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