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September 2013 Rainbow Ramsey Theorem for triples is strictly weaker than the Arithmetical Comprehension Axiom
Wei Wang
J. Symbolic Logic 78(3): 824-836 (September 2013). DOI: 10.2178/jsl.7803070

Abstract

We prove that $\operatorname{RCA}_0 + \operatorname{RRT}^3_2 \nvdash \operatorname{ACA}_0$ where $\operatorname{RRT}^3_2$ 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 $\operatorname{RCA}_0 + \operatorname{RRT}^4_2 \vdash \operatorname{ACA}_0$ and obtain some partial answer.

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Wei Wang. "Rainbow Ramsey Theorem for triples is strictly weaker than the Arithmetical Comprehension Axiom." J. Symbolic Logic 78 (3) 824 - 836, September 2013. https://doi.org/10.2178/jsl.7803070

Information

Published: September 2013
First available in Project Euclid: 6 January 2014

zbMATH: 1300.03013
MathSciNet: MR3135500
Digital Object Identifier: 10.2178/jsl.7803070

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Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 3 • September 2013
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