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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

Wei Wang
Wei Wang*
Affiliation:
Institute of Logic and Cognition and Department of Philosophy, Sun Yat-Sen University, 135 Xingang XI Road, Guangzhou 510275, P.R. China, E-mail: wwang.cn@gmail.com
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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.

Keywords

03B3003F3503D3203D80
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 824 - 836
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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