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Bounding nonsplitting enumeration degrees

Published online by Cambridge University Press:  12 March 2014

Thomas F. Kent  and
Andrea Sorbi
Thomas F. Kent
Affiliation:
Dipartimento di Scienze Matematiche ed Informatiche, “Roberto Magari”, Pian Dei Mantellini 44, 53100 Siena, Italy. E-mail: kent@unisi.it
Andrea Sorbi
Affiliation:
Dipartimento di Scienze Matematiche ed Informatiche, “Roberto Magari”, Pian Dei Mantellini 44, 53100 Siena, Italy. E-mail: sorbi@unisi.it
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Abstract

We show that every nonzero enumeration degree bounds a nonsplitting nonzero enumeration degree.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1405 - 1417
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

[1]Ahmad, Seema, Some results on the structure of the Σ2 enumeration degrees, Ph.D. thesis, Simon Fraser University, 1989.Google Scholar
[2]Ahmad, Seema, Embedding the diamond in the Σ2 enumeration degrees, this Journal, vol. 56 (1991), no. 1, pp. 195–212.Google Scholar
[3]Ahmad, Seema and Lachlan, Alistair H., Some special pairs of Σ2 e-degrees, Mathematical Logic Quarterly, vol. 44 (1998), no. 4, pp. 431–449.CrossRefGoogle Scholar
[4]Arslanov, Marat M., Kalimullin, Iskander Sh., and Cooper, S. Barry, Splitting properties of total enumeration degrees, Algebra and Logic, vol. 42 (2003), no. 1, pp. 1–13.CrossRefGoogle Scholar
[5]Cooper, S. Barry, Partial degrees and the density problem. II, The enumeration degrees of the Σ2 sets are dense, this Journal, vol. 49 (1984), no. 2, pp. 503–513.Google Scholar
[6]Lachlan, Alistair H., Lower bounds for pairs of recursively enumerable degrees, Proceedings of the London Mathematical Society. Third Series, vol. 16 (1966), pp. 537–569.CrossRefGoogle Scholar
[7]Lachlan, Alistair H. and Shore, Richard A., The n-rea enumeration degrees are dense, Archive for Mathematical Logic, vol. 31 (1992), no. 4, pp. 277–285.CrossRefGoogle Scholar
[8]McEvoy, Kevin, Jumps of quasiminimal enumeration degrees, this Journal, vol. 50 (1985), no. 3, pp. 839–848.Google Scholar
[9]McEvoy, Kevin and Cooper, S. Barry, On minimal pairs of enumeration degrees, this Journal, vol. 50 (1985), no. 4, pp. 983–1001.Google Scholar
[10]Sacks, Gerald E., On the degrees less than 0′, Annals of Mathematics. Second Series, vol. 77 (1963), pp. 211–231.CrossRefGoogle Scholar
[11]Soare, Robert I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1987.CrossRefGoogle Scholar