Journal of Symbolic Logic 49 (2):376-400 (1984)
Solovay has shown that if F: [ω] ω → 2 is a clopen partition with recursive code, then there is an infinite homogeneous hyperarithmetic set for the partition (a basis result). Simpson has shown that for every 0 α , where α is a recursive ordinal, there is a clopen partition F: [ω] ω → 2 such that every infinite homogeneous set is Turing above 0 α (an anti-basis result). Here we refine these results, by associating the "order type" of a clopen set with the Turing complexity of the infinite homogeneous sets. We also consider the Nash-Williams barrier theorem and its relation to the clopen Ramsey theorem
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Recursive Well-Founded Orderings.Keh-Hsun Chen - 1978 - Annals of Mathematical Logic 13 (2):117-147.
Citations of this work BETA
No citations found.
Similar books and articles
A Δ02 Set with No Infinite Low Subset in Either It or its Complement.Rod Downey, Denis R. Hirschfeldt, Steffen Lempp & Reed Solomon - 2001 - Journal of Symbolic Logic 66 (3):1371 - 1381.
A Baire-Type Theorem for Cardinals.Kurt Wolfsdorf - 1983 - Journal of Symbolic Logic 48 (4):1082-1089.
An Effective Proof That Open Sets Are Ramsey.Jeremy Avigad - 1998 - Archive for Mathematical Logic 37 (4):235-240.
Stable Ramsey's Theorem and Measure.Damir D. Dzhafarov - 2010 - Notre Dame Journal of Formal Logic 52 (1):95-112.
On the Strength of Ramsey's Theorem for Pairs.Peter A. Cholak, Carl G. Jockusch & Theodore A. Slaman - 2001 - Journal of Symbolic Logic 66 (1):1-55.
On the Ramsey Property for Sets of Reals.Ilias G. Kastanas - 1983 - Journal of Symbolic Logic 48 (4):1035-1045.
Effective Versions of Ramsey's Theorem: Avoiding the Cone Above 0'.Tamara Lakins Hummel - 1994 - Journal of Symbolic Logic 59 (4):1301-1325.
A Generalization of the Limit Lemma and Clopen Games.Peter Clote - 1986 - Journal of Symbolic Logic 51 (2):273-291.
Added to index2009-01-28
Total downloads5 ( #595,594 of 2,163,980 )
Recent downloads (6 months)1 ( #348,017 of 2,163,980 )
How can I increase my downloads?