Reverse mathematics and Ramsey's property for trees

Journal of Symbolic Logic 75 (3):945-954 (2010)
  Copy   BIBTEX

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 $B\sum_{2}^{0}$ , 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]

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,998

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

On the Indecomposability of $\omega^{n}$.Jared R. Corduan & François G. Dorais - 2012 - Notre Dame Journal of Formal Logic 53 (3):373-395.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.
Reverse mathematics: the playground of logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Ramsey and the notion of arbitrary function.Gabriel Sandu - 2005 - In Maria J. Frapolli Sanz (ed.), F. P. Ramsey. Critical Reassessments. Continuum International Publishing Group. pp. 237-256.
On the Ramsey property for sets of reals.Ilias G. Kastanas - 1983 - Journal of Symbolic Logic 48 (4):1035-1045.
Analytic cut trees.Carlo Cellucci - 2000 - Logic Journal of the IGPL 8 (6):733-750.
On Scott and Karp trees of uncountable models.Tapani Hyttinen & Jouko Väänänen - 1990 - Journal of Symbolic Logic 55 (3):897-908.
Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2011 - Notre Dame Journal of Formal Logic 52 (1):95-112.

Analytics

Added to PP
2010-09-12

Downloads
37 (#431,672)

6 months
11 (#238,333)

Historical graph of downloads
How can I increase my downloads?