Ramsey’s theorem for trees: the polarized tree theorem and notions of stability [Book Review]

Archive for Mathematical Logic 49 (3):399-415 (2010)
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Abstract

We formulate a polarized version of Ramsey’s theorem for trees. For those exponents greater than 2, both the reverse mathematics and the computability theory associated with this theorem parallel that of its linear analog. For pairs, the situation is more complex. In particular, there are many reasonable notions of stability in the tree setting, complicating the analysis of the related results

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Citations of this work

Open Questions in Reverse Mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse Mathematics and Ramsey Properties of Partial Orderings.Jared Corduan & Marcia Groszek - 2016 - Notre Dame Journal of Formal Logic 57 (1):1-25.
The Strength of the Tree Theorem for Pairs in Reverse Mathematics.Ludovic Patey - 2016 - Journal of Symbolic Logic 81 (4):1481-1499.

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