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September 2010 Reverse mathematics and Ramsey's property for trees
Jared Corduan, Marcia J. Groszek, Joseph R. Mileti
J. Symbolic Logic 75(3): 945-954 (September 2010). DOI: 10.2178/jsl/1278682209

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].

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Jared Corduan. Marcia J. Groszek. Joseph R. Mileti. "Reverse mathematics and Ramsey's property for trees." J. Symbolic Logic 75 (3) 945 - 954, September 2010. https://doi.org/10.2178/jsl/1278682209

Information

Published: September 2010
First available in Project Euclid: 9 July 2010

zbMATH: 1203.03018
MathSciNet: MR2723776
Digital Object Identifier: 10.2178/jsl/1278682209

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 3 • September 2010
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