Reverse mathematics and Ramsey's property for trees-Reference-Cited by-同舟云学术

Reverse mathematics and Ramsey's property for trees

Published:2010-09 Issue:3 Volume:75 Page:945-954
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

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

Abstract

AbstractWe 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 . 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].

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference6 articles.

1. Hirst J. , personal communication (e-mail 06 12, 2008).

2. Hirst J. , Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, The Pennsylvania State University, 1987.

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