Effectiveness for infinite variable words and the dual Ramsey theorem (Q701747)

The authors apply techniques of reverse mathematics to the dual Ramsey theorem, providing partial answers to questions posed by \textit{H. Friedman} and \textit{S. G. Simpson} [Contemp. Math. 257, 127--144 (2000; Zbl 0967.03050)]. In particular, they show that the open dual Ramsey theorem implies ACA\(_0\). They also analyze combinatorial statements about variable words and ordered variable words which are related to central lemmas in \textit{T. J. Carlson} and \textit{S. G. Simpson}'s proof of the dual Ramsey theorem [Adv. Math. 53, 265--290 (1984; Zbl 0564.05005)].