Rainbow Ramsey theorem for triples is strictly weaker than the Arithmetic Comprehension Axiom

Wei Wang

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arXiv · 1303.3327

Rainbow Ramsey theorem for triples is strictly weaker than the Arithmetic Comprehension Axiom

Wei Wang

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Abstract

We prove that $\RCA + \RRT^3_2 \not\vdash \ACA$ where $\RRT^3_2$ 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 $\RCA + \RRT^4_2 \vdash \ACA$ and obtain some partial answer.

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BibTeX RIS

Wei Wang. 2013-03-14. Rainbow Ramsey theorem for triples is strictly weaker than the Arithmetic Comprehension Axiom. https://arxiv.org/abs/1303.3327

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