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Definability in the recursively enumerable degrees

André Nies, Richard A. Shore & Theodore A. Slaman

Bulletin of Symbolic Logic 2 (4):392-404 (1996)

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The existence of high nonbounding degrees in the difference hierarchy.Chi Tat Chong, Angsheng Li & Yue Yang - 2006 - Annals of Pure and Applied Logic 138 (1):31-51.details We study the jump hierarchy of d.c.e. Turing degrees and show that there exists a high d.c.e. degree d which does not bound any minimal pair of d.c.e. degrees. Download Export citation Bookmark 1 citation
On the Definable Ideal Generated by Nonbounding C.E. Degrees.Liang Yu & Yue Yang - 2005 - Journal of Symbolic Logic 70 (1):252 - 270.details Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far. Download Export citation Bookmark 3 citations

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