The metamathematics of Stable Ramsey’s Theorem for Pairs

Chong, C.; Slaman, Theodore; Yang, Yue

doi:10.1090/S0894-0347-2014-00789-X

The metamathematics of Stable Ramsey’s Theorem for Pairs
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by C. T. Chong, Theodore A. Slaman and Yue Yang;

J. Amer. Math. Soc. 27 (2014), 863-892

DOI: https://doi.org/10.1090/S0894-0347-2014-00789-X

Published electronically: March 25, 2014

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Abstract:

We show that, over the base theory $\textit {RCA}_0$, Stable Ramsey’s Theorem for Pairs implies neither Ramsey’s Theorem for Pairs nor $\Sigma ^0_2$-induction.

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