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Rainbow Ramsey Theorem for Triples is Strictly Weaker than the Arithmetical Comprehension Axiom
Published online by Cambridge University Press: 12 March 2014
Abstract
We 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.
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- Copyright © Association for Symbolic Logic 2013
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