The Strength of the Rainbow Ramsey Theorem

Journal of Symbolic Logic 74 (4):1310 - 1324 (2009)
  Copy   BIBTEX


The Rainbow Ramsey Theorem is essentially an "anti-Ramsey" theorem which states that certain types of colorings must be injective on a large subset (rather than constant on a large subset). Surprisingly, this version follows easily from Ramsey's Theorem, even in the weak system RCA₀ of reverse mathematics. We answer the question of the converse implication for pairs, showing that the Rainbow Ramsey Theorem for pairs is in fact strictly weaker than Ramsey's Theorem for pairs over RCA₀. The separation involves techniques from the theory of randomness by showing that every 2-random bounds an ω-model of the Rainbow Ramsey Theorem for pairs. These results also provide as a corollary a new proof of Martin's theorem that the hyperimmune degrees have measure one



    Upload a copy of this work     Papers currently archived: 92,150

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

Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2011 - Notre Dame Journal of Formal Logic 52 (1):95-112.
Ramsey's Theorem and Cone Avoidance.Damir D. Dzhafarov & Carl G. Jockusch - 2009 - Journal of Symbolic Logic 74 (2):557-578.
On the Ramsey property for sets of reals.Ilias G. Kastanas - 1983 - Journal of Symbolic Logic 48 (4):1035-1045.
A Simple Proof and Some Difficult Examples for Hindman's Theorem.Henry Towsner - 2012 - Notre Dame Journal of Formal Logic 53 (1):53-65.
Ramsey’s representation theorem.Richard Bradley - 2004 - Dialectica 58 (4):483–497.
Reverse mathematics and a Ramsey-type König's Lemma.Stephen Flood - 2012 - Journal of Symbolic Logic 77 (4):1272-1280.


Added to PP

64 (#253,767)

6 months
19 (#136,833)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Cohesive sets and rainbows.Wei Wang - 2014 - Annals of Pure and Applied Logic 165 (2):389-408.
Degrees bounding principles and universal instances in reverse mathematics.Ludovic Patey - 2015 - Annals of Pure and Applied Logic 166 (11):1165-1185.

View all 8 citations / Add more citations

References found in this work

On the Strength of Ramsey's Theorem.David Seetapun & Theodore A. Slaman - 1995 - Notre Dame Journal of Formal Logic 36 (4):570-582.
Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Computability Theory.Barry Cooper - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).

Add more references