Ordered Variable Word theorem does not imply RT^2_2, admits low2 computable solutions, and yields Carlson-Simpson and Open Dual Ramsey over ACA0.
Hirschfeldt.Slicing the truth, volume 28 ofLecture Notes Se- ries
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Generalizations of Free Set, Thin Set, and Rainbow Ramsey theorems are proved for the Schreier barrier, with computability analysis showing that the first two can code ∅^(ω) while the third does not code 0'.
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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.
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Ramsey-like theorems for the Schreier barrier
Generalizations of Free Set, Thin Set, and Rainbow Ramsey theorems are proved for the Schreier barrier, with computability analysis showing that the first two can code ∅^(ω) while the third does not code 0'.