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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: [email protected]
Decheng Ding
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: [email protected]
Wei Wang*
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: [email protected]
Liang Yu
Affiliation:
Department of Mathematics, Nanjing University, 22 Hankou Road, Nanjing 210093, P.R., China, E-mail: [email protected]
*
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore
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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

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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