Ramsey’s Theorem and cone avoidance, this
| Venue: | JOURNAL |
| Citations: | 2 - 2 self |
BibTeX
@ARTICLE{Dzhafarov_ramsey’stheorem,
author = {Damir D. Dzhafarov and Carl and G. Jockusch},
title = {Ramsey’s Theorem and cone avoidance, this},
journal = {JOURNAL},
year = {},
pages = {557--578}
}
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Abstract
Abstract. It was shown by Cholak, Jockusch, and Slaman that every computable 2-coloring of pairs admits an infinite low2 homogeneous set H. We answer a question of the same authors by showing that H may be chosen to satisfy in addition C ̸≤T H, where C is a given noncomputable set. This is shown by analyzing a new and simplified proof of Seetapun’s cone avoidance theorem for Ramsey’s theorem. We then extend the result to show that every computable 2-coloring of pairs admits a pair of low2 infinite homogeneous sets whose degrees form a minimal pair. 1.
Citations
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