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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The metamathematics of Stable Ramsey's Theorem for Pairs


Authors: C. T. Chong, Theodore A. Slaman and Yue Yang
Journal: J. Amer. Math. Soc. 27 (2014), 863-892
MSC (2010): Primary 03B30, 03F35, 03D80; Secondary 05D10
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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Additional Information

C. T. Chong
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076
Email: chongct@math.nus.edu.sg

Theodore A. Slaman
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
Email: slaman@math.berkeley.edu

Yue Yang
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119076
Email: matyangy@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0894-0347-2014-00789-X
PII: S 0894-0347(2014)00789-X
Keywords: Reverse mathematics, $RCA_0$, $\Sigma^0_2$-bounding, Ramsey's Theorem for Pairs, Stable Ramsey's Theorem for Pairs
Received by editor(s): September 1, 2012
Received by editor(s) in revised form: August 17, 2013
Published electronically: March 25, 2014
Article copyright: © Copyright 2014 American Mathematical Society