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The degrees below a 1-generic degree < 0′

Published online by Cambridge University Press:  12 March 2014

Christine Ann Haught
Christine Ann Haught*
Affiliation:
Mathematical Sciences, Loyola University of Chicago, Chicago, Illinois 60626
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Abstract

It is shown that the nonrecursive predecessors of a 1-generic degree < 0′ are all 1-generic. As a corollary, it is shown that the 1-generic degrees are not densely ordered.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 51 , Issue 3 , September 1986, pp. 770 - 777
Copyright
Copyright © Association for Symbolic Logic 1986

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References

REFERENCES

[1]Chong, C. T. and Jockusch, C. G. Jr., Minimal degrees and 1-generic sets below 0′, Computation and proof theory (proceedings of Logic Colloquium '83, part 2; Richter, M. M.et al., editors), Lecture Notes in Mathematics, vol. 1104, Springer-Verlag, Berlin, 1985, pp. 63–77.Google Scholar
[2]Haught, C. A., Turing and truth table degrees of 1-generic and recursively enumerable sets, Ph. D. Thesis, Cornell University, Ithaca, New York, 1985.Google Scholar
[3]Jockusch, C. G. Jr., Degrees of generic sets, Recursion theory, its generalisations and applications (proceedings of Logic Colloquium '79; Drake, F. R. and Wainer, S. S., editors), London Mathematical Society Lecture Note Series, vol. 45, Cambridge University Press, Cambridge, 1980, pp. 110–139.CrossRefGoogle Scholar
[4]Kleene, S. C. and Post, E. L., The upper semilattice of degrees of recursive unsolvability, Annals of Mathematics, ser. 2, vol. 59 (1954), pp. 379–407.CrossRefGoogle Scholar
[5]Yates, C. E. M., Initial segments of the degrees of unsolvability. Part II: Minimal degrees, this Journal, vol. 35 (1970), pp. 243–266.Google Scholar
[6]Yates, C. E. M., Banach-Mazur games, comeager sets and degrees of unsolvability, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 79 (1976), pp. 195–220.CrossRefGoogle Scholar