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Title: On the role of the collection principle for ∑2 0 -formulas in second-order reverse mathematics
Authors: Chong, C.T. 
Lempp, S.
Yang, Y. 
Keywords: ∑2 0 -bounding
Bi-tame cut
Linear order
Ramsey's theorem
Reverse mathematics
Tame cut
Issue Date: Mar-2010
Citation: Chong, C.T., Lempp, S., Yang, Y. (2010-03). On the role of the collection principle for ∑2 0 -formulas in second-order reverse mathematics. Proceedings of the American Mathematical Society 138 (3) : 1093-1100. ScholarBank@NUS Repository.
Abstract: We show that the principle PART from Hirschfeldt and Shore is equivalent to the ∑2 0 -Bounding principle B∑2 0 over RCA0, answering one of their open questions. Furthermore, we also fill a gap in a proof of Cholak, Jockusch and Slaman by showing that D2 2 implies B∑2 0 and is thus indeed equivalent to Stable Ramsey's Theorem for Pairs (SRT2 2 ). This also allows us to conclude that the combinatorial principles IPT 2 2 , SPT2 2 and SIPT2 2 defined by Dzhafarov and Hirst all imply B∑2 0 and thus that SPT2 2 and SIPT2 2 are both equivalent to SRT2 2 as well. Our proof uses the notion of a bi-tame cut, the existence of which we show to be equivalent, over RCA0, to the failure of B∑2 0 © 2009 American Mathematical Society.
Source Title: Proceedings of the American Mathematical Society
ISSN: 00029939
DOI: 10.1090/S0002-9939-09-10115-6
Appears in Collections:Staff Publications

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