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On the definable ideal generated by nonbounding c.e. degrees

Published online by Cambridge University Press:  12 March 2014

Liang Yu  and
Yue Yang
Liang Yu
Affiliation:
School of Mathematics and Computing Sciences, Victoria University of Wellington, Wellington, New Zealand, E-mail: yuliang@mcs.vuw.ac.nz
Yue Yang
Affiliation:
Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, Singapore, E-mail: matyangy@leonis.nus.edu.sg
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Abstract

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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 252 - 270
Copyright
Copyright © Association for Symbolic Logic 2005

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References

REFERENCES

[1]Ambos-Spies, Klaus and Soare, Robert I., The recursively enumerable degrees have infinitely many one-types, Annals of Pure and Applied Logic, vol. 44 (1989), no. 1-2, pp. 1–23.CrossRefGoogle Scholar
[2]Fejer, P. A. and Soare, Robert I., The plus-cupping theorem for the recursively enumerable degrees, Logic year 1979–80: University of Connecticut, 1981, pp. 49–62.CrossRefGoogle Scholar
[3]Li, Angsheng, Slaman, Theodore A., and Yang, Yue, A nonlow2 c.e. degree which bounds no diamond bases, to appear.Google Scholar
[4]Nies, André, private communication.Google Scholar
[5]Nies, André, Parameter definability in the r.e. degrees, Journal of Mathematical Logic, vol. 3 (2003), no. 1, pp. 37–65.CrossRefGoogle Scholar
[6]Nies, André, Shore, Richard A., and Slaman, Theodore A., Definability in the recursively enumerable degrees, The Bulletin of Symbolic Logic, vol. 2 (1996), no. 4, pp. 392–404.CrossRefGoogle Scholar
[7]Nies, André, Shore, Richard A., and Slaman, Theodore A., Interpretability and definability in the recursively enumerable degrees, Proceedings of the London Mathematical Society, vol. 77 (1998), no. 2, pp. 241–291.CrossRefGoogle Scholar
[8]Shore, Richard A., Natural definability in degree structures, Computability theory and its applications (Boulder, CO, 1999), American Mathematical Society, Providence, RI, 2000, pp. 255–271.CrossRefGoogle Scholar
[9]Soare, Robert I., Recursively enumerable sets and degrees, Springer–Verlag, Heidelberg, 1987.CrossRefGoogle Scholar