Ordered Variable Word theorem does not imply RT^2_2, admits low2 computable solutions, and yields Carlson-Simpson and Open Dual Ramsey over ACA0.
The reverse mathematics of Carlson’s theorem for located words.arXiv preprint arXiv:2208.03152, 2022
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The reverse mathematics of the Ordered Variable Word theorem
Ordered Variable Word theorem does not imply RT^2_2, admits low2 computable solutions, and yields Carlson-Simpson and Open Dual Ramsey over ACA0.