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Cappable CEA sets and Ramsey’s theorem. (English) Zbl 1280.03041
Arai, Toshiyasu (ed.) et al., Proceedings of the 11th Asian logic conference in honor of Professor Chong Chitat on his 60th birthday, National University of Singapore, Singapore, June 22–27, 2009. Hackensack, NJ: World Scientific (ISBN 978-981-4360-53-1/hbk; 978-981-4360-54-8/ebook). 114-127 (2012).
The authors begin a search for degree-theoretic properties that might be used to separate Ramsey’s theorem for pairs from its stable version in the sense of reverse mathematics. They obtain the following result.
Theorem. There is a computable stable coloring of pairs that does not have a homogeneous set computable from a \(c\)-cappable 2-CEA set.
For the entire collection see [Zbl 1253.03002].
MSC:
03C57 Computable structure theory, computable model theory
03D45 Theory of numerations, effectively presented structures
03C55 Set-theoretic model theory
03D25 Recursively (computably) enumerable sets and degrees
03B30 Foundations of classical theories (including reverse mathematics)
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