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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.
|Keywords:||∑2 0 -bounding
|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. https://doi.org/10.1090/S0002-9939-09-10115-6||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||URI:||http://scholarbank.nus.edu.sg/handle/10635/103836||ISSN:||00029939||DOI:||10.1090/S0002-9939-09-10115-6|
|Appears in Collections:||Staff Publications|
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