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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Abstract

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].

Article information

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

Dates
First available in Project Euclid: 9 July 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1278682209

Digital Object Identifier
doi:10.2178/jsl/1278682209

Mathematical Reviews number (MathSciNet)
MR2723776

Zentralblatt MATH identifier
1203.03018

Citation

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. https://projecteuclid.org/euclid.jsl/1278682209


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