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On the Cantor-Bendixon rank of recursively enumerable sets

Published online by Cambridge University Press:  12 March 2014

Peter Cholak  and
Rod Downey
Peter Cholak*
Affiliation:
Department of Mathematics, 4009 Angell Hall, University of Michigan,Ann Arbor, Michigan, 48109
Rod Downey
Affiliation:
Victoria University of Wellington,P.O. Box 600, Wellington, New Zealand, E-mail: [email protected]
*
Cornell University, Ithaca, New York14853, E-mail: [email protected]
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Abstract

The main result of this paper is to show that for every recursive ordinal α ≠ 0 and for every nonrecursive r.e. degree d there is a r.e. set of rank α and degree d.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 2 , June 1993 , pp. 629 - 640
Copyright
Copyright © Association for Symbolic Logic 1993

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References

REFERENCES

[CCSSW86] Cenzer, D., Clote, P., Smith, R., Soare, R., and Wainer, S., Members of countable classes, Annals of Pure and Applied Logic, vol. 31 (1986). pp. 145–163.CrossRefGoogle Scholar
[CDJS93] Cenzer, D., Downey, R., Jockusch, C., and Soare, R., Countable thin -classes, Annals of Pure Applied Logic, vol. 59 (1993), pp. 79–140.CrossRefGoogle Scholar
[CS89] Cenzer, D., and Smith, R., The ranked members of a set, this Journal, vol. 54 (1989), pp. 975–991.Google Scholar
[DM58] Dekker, J. and Myhill, J., Retraceable sets, Canadian Journal of Mathematics, vol. 10(1958), pp. 357–373.CrossRefGoogle Scholar
[Do9] Downey, R. G., On classes and their ranked points, Notre Dame Journal of Formal Logic, vol. 32 (1991), no. 4, pp. 499–512.CrossRefGoogle Scholar
[Kr59] Kreisel, G., Analysis of the Cantor-Bendixon theorem by means of the analytic hierarchy, Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 7 (1959), pp. 621–626.Google Scholar
[Ro68] Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1968.Google Scholar
[Od89] Odifreddi, P., Classical recursive theory, North-Holland, Amsterdam, 1989.Google Scholar
[So87] Soare, R., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Omega Series, Springer-Verlag, Berlin, Heidelberg, New York, and Tokyo, 1987.CrossRefGoogle Scholar