Please use this identifier to cite or link to this item:
|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|
|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|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Aug 14, 2018
WEB OF SCIENCETM
checked on Aug 6, 2018
checked on Jun 1, 2018
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.