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Effectiveness for infinite variable words and the Dual Ramsey Theorem

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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].

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References

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, Indiana, 47405-5701, USA

    Joseph S. Miller

  2. Department of Mathematics, University of Connecticut Storrs, Connecticut, 06269-3009, USA

    Reed Solomon

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  1. Joseph S. Miller
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  2. Reed Solomon
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Correspondence to Joseph S. Miller.

Additional information

The first author’s research is partially supported by an NSF VIGRE Grant at Indiana University. The second author’s research is partially supported by an NSF Postdoctoral Fellowship.

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Miller, J., Solomon, R. Effectiveness for infinite variable words and the Dual Ramsey Theorem. Arch. Math. Logic 43, 543–555 (2004). https://doi.org/10.1007/s00153-004-0216-4

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  • DOI: https://doi.org/10.1007/s00153-004-0216-4

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