Rainbow Ramsey Theorem for Triples is Strictly Weaker than the Arithmetical Comprehension Axiom
AbstractWe prove that RCA0 + RRT ⊬ ACA0 where RRT is the Rainbow Ramsey Theorem for 2-bounded colorings of triples. This reverse mathematical result is based on a cone avoidance theorem, that every 2-bounded coloring of pairs admits a cone-avoiding infinite rainbow, regardless of the complexity of the given coloring. We also apply the proof of the cone avoidance theorem to the question whether RCA0 + RRT ⊦ ACA0 and obtain some partial answer.
2015 ◽
Vol 36
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pp. 82-103
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1982 ◽
Vol 21
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pp. 15-22
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1977 ◽
Vol 16
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pp. 234-240
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1969 ◽
Vol 8
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pp. 84-90
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