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The density of the meet-inaccessible r. e. degrees

Published online by Cambridge University Press:  12 March 2014

Zhang Qinglong
Zhang Qinglong*
Affiliation:
Institute of Software, Academia Sinica, Beijing 100080, China
*
Department of Mathematics, Statistics and Computer Science, University of Illinois, at Chicago, Chicago, Illinois 60680.
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Abstract

In this paper it is shown that the meet-inaccessible degrees are dense in R. The construction uses an 0′-priority argument. As a consequence, the meet-inaccessible degrees and the meet-accessible degrees give a partition of R into two sets, either of which is a nontrivial dense subset of R and generates R − {0} under joins (thus an automorphism base of R).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 2 , June 1992 , pp. 585 - 596
Copyright
Copyright © Association for Symbolic Logic 1992

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References

REFERENCES

[1]Ambos-Spies, K., Generators of the recursively enumerable degrees, Recursion theory week (Oberwolfach, 1984; Ebbinghaus, H.-D.et al., editors), Lecture Notes in Mathematics, vol. 1141, Springer-Verlag, Berlin, 1985, pp. 1–28.Google Scholar
[2]Fejer, P. A., Branching degrees above low degrees, Transactions of the American Mathematical Society, vol. 273 (1982), pp. 157–180.CrossRefGoogle Scholar
[3]Fejer, P. A., The density of the nonbranching degrees, Annals of Mathematical Logic, vol. 24 (1983), pp. 113–130.Google Scholar
[4]Lachlan, A. H., Lower bounds for pairs of recursively enumerable degrees, Proceedings of the London Mathematical Society, ser. 3, vol. 16 (1966), pp. 537–569.CrossRefGoogle Scholar
[5]Robinson, R. W., Interpolation and embedding in the recursively enumerable degrees, Annals of Mathematics, ser. 2, vol. 93 (1971), pp. 285–314.CrossRefGoogle Scholar
[6]Soare, R. I., Computational complexity, speedable and levelable sets, this Journal, vol. 42 (1977), pp. 545–563.Google Scholar
[7]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar