Ramsey’s theorem for trees: the polarized tree theorem and notions of stability [Book Review]

Archive for Mathematical Logic 49 (3):399-415 (2010)
  Copy   BIBTEX

Abstract

We formulate a polarized version of Ramsey’s theorem for trees. For those exponents greater than 2, both the reverse mathematics and the computability theory associated with this theorem parallel that of its linear analog. For pairs, the situation is more complex. In particular, there are many reasonable notions of stability in the tree setting, complicating the analysis of the related results

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

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

The polarized Ramsey’s theorem.Damir D. Dzhafarov & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (2):141-157.
Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2011 - Notre Dame Journal of Formal Logic 52 (1):95-112.
The Strength of the Rainbow Ramsey Theorem.Barbara F. Csima & Joseph R. Mileti - 2009 - Journal of Symbolic Logic 74 (4):1310 - 1324.
Partitions of trees and $${{\sf ACA}^\prime_{0}}$$.Bernard A. Anderson & Jeffry L. Hirst - 2009 - Archive for Mathematical Logic 48 (3-4):227-230.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.
On the strength of Ramsey's theorem without Σ1 -induction.Keita Yokoyama - 2013 - Mathematical Logic Quarterly 59 (1-2):108-111.
On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
A Simple Proof and Some Difficult Examples for Hindman's Theorem.Henry Towsner - 2012 - Notre Dame Journal of Formal Logic 53 (1):53-65.

Analytics

Added to PP
2013-11-23

Downloads
66 (#222,759)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Open questions in reverse mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse Mathematics and Ramsey Properties of Partial Orderings.Jared Corduan & Marcia Groszek - 2016 - Notre Dame Journal of Formal Logic 57 (1):1-25.
The strength of the tree theorem for pairs in reverse mathematics.Ludovic Patey - 2016 - Journal of Symbolic Logic 81 (4):1481-1499.

Add more citations