Journal of Symbolic Logic

Reverse mathematics and Ramsey's property for trees

Jared Corduan, Marcia J. Groszek, and Joseph R. Mileti

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We show, relative to the base theory RCA₀: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA₀. Ramsey's Theorem for singletons for the complete binary tree is stronger than BΣ⁰₂, hence stronger than Ramsey's Theorem for singletons for ω. These results lead to extensions of results, or answers to questions, of Chubb, Hirst, and McNicholl [3].

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J. Symbolic Logic, Volume 75, Issue 3 (2010), 945-954.

First available in Project Euclid: 9 July 2010

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Corduan, Jared; Groszek, Marcia J.; Mileti, Joseph R. Reverse mathematics and Ramsey's property for trees. J. Symbolic Logic 75 (2010), no. 3, 945--954. doi:10.2178/jsl/1278682209.

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