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].

• Type: Journal
• Year: 2004
• Where: AML
• Authors: Joseph S. Miller, Reed Solomon
• Keywords: AML 2004, Combinatorial Principles, Dual Ramsey Theorem, Reverse Mathematics