Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-26T12:29:48.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Bounding non-GL2 and R.E.A.

Published online by Cambridge University Press:  12 March 2014

Klaus Ambos-Spies ,
Decheng Ding ,
Wei Wang  and
Liang Yu
Klaus Ambos-Spies
Affiliation:
Institut für Informatik, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany, E-mail: ambos@math.uni-heidelberg.de
Decheng Ding
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: dcding@nju.edu.cn
Wei Wang*
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: wwang.cn@gmail.com
Liang Yu
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: yuliang.nju@gmail.com
*
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that every Turing degree a bounding some non-GL2 degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.

Keywords

Generalized high/low hierarchiesrecursively enumerable in and abovegeneric degree
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 989 - 1000
Copyright
Copyright © Association for Symbolic Logic 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Harizanov, Valentina S., Turing degrees of certain isomorphic images of computable relations, Ann. Pure Appl. Logic, vol. 93 (1998), no. 1-3, pp. 103–113.CrossRefGoogle Scholar
[2]Hirschfeldt, Denis R. and Shore, Richard A., Combinatorial principles weaker than Ramsey's theorem for pairs, this Journal, vol. 72 (2007), no. 1, pp. 171–206.Google Scholar
[3]Jockusch, Carl G. Jr, Degrees of generic sets, Recursion theory: Its generalizations and applications. Proceedings of Logic Colloquium '79, Leeds, August 1979 (Cambridge, U. K.) (Drake, F. R. and Wainer, S. S., editors), Cambridge University Press, 1980, pp. 110–139.Google Scholar
[4]Jockusch, Carl G. Jr. and Posner, David B., Double jumps of minimal degrees, this Journal, vol. 43 (1978), no. 4, pp. 715–724.Google Scholar
[5]Kumabe, Masahiro, Relative recursive enumerability of generic degrees, this Journal, vol. 56 (1991), no. 3, pp. 1075–1084.Google Scholar
[6]Kumabe, Masahiro, A 1-generic degree with a strong minimal cover, this Journal, vol. 65 (2000), no. 3, pp. 1395–1442.Google Scholar
[7]Lerman, M., Degrees of unsolvability, Perspectives in Mathematical Logic, Springer-Verlag, Heidelberg, 1983, 307 pages.CrossRefGoogle Scholar
[8]Martin, D. A., Classes of recursively enumerable sets and degrees of unsolvability, Z. Math. Logik Grundlag. Math., vol. 12 (1966), pp. 295–310.CrossRefGoogle Scholar
[9]Robinson, R. W., Jump restricted interpolation in the recursively enumerable degrees, Ann. of Math. (2), vol. 93 (1971), pp. 586–596.CrossRefGoogle Scholar
[10]Sasso, L. P., A minimal degree not realizing least possible jump, this Journal, vol. 39 (1974), pp. 571–574.Google Scholar
[11]Soare, Robert I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer–Verlag, Heidelberg, 1987.CrossRefGoogle Scholar
[12]Yu, Liang, Lowness for genericity, Arch. Math. Logic, vol. 45 (2006), no. 2, pp. 233–238.CrossRefGoogle Scholar