Journal of Symbolic Logic

On Σ₁-structural differences among finite levels of the Ershov hierarchy

Yue Yang and Liang Yu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We show that the structure ℛ of recursively enumerable degrees is not a Σ₁-elementary substructure of 𝒟n, where 𝒟n (n>1) is the structure of n-r.e. degrees in the Ershov hierarchy.

Article information

Source
J. Symbolic Logic, Volume 71, Issue 4 (2006), 1223-1236.

Dates
First available in Project Euclid: 20 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1164060453

Digital Object Identifier
doi:10.2178/jsl/1164060453

Mathematical Reviews number (MathSciNet)
MR2275857

Zentralblatt MATH identifier
1112.03038

Subjects
Primary: 03D25: Recursively (computably) enumerable sets and degrees

Citation

Yang, Yue; Yu, Liang. On Σ₁-structural differences among finite levels of the Ershov hierarchy. J. Symbolic Logic 71 (2006), no. 4, 1223--1236. doi:10.2178/jsl/1164060453. https://projecteuclid.org/euclid.jsl/1164060453


Export citation

References

  • Marat M. Arslanov, Structural properties of the degrees below $0'$, Doklady Akademiia Nauk SSSR, (1985), pp. 270--273.
    Mathematical Reviews (MathSciNet): MR804113
  • Marat M. Arslanov, Iskander Sh. Kalimullin, and Steffen Lempp, On Downey's conjecture, preprint, 2005.
  • S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp, and Robert I. Soare, The d.r.e. degrees are not dense, Annals of Pure and Applied Logic, vol. 55 (1991), no. 2, pp. 125--151.
    Mathematical Reviews (MathSciNet): MR1141717
    Digital Object Identifier: doi:10.1016/0168-0072(91)90005-7
    Zentralblatt MATH: 0756.03020
  • Rodney G. Downey, Intervals and sublattices of the recursively enumerable $\textbf\upshape T$- and w-degrees, part I: Density, Annals of Pure and Applied Logic, vol. 49 (1989), pp. 1--27.
    Mathematical Reviews (MathSciNet): MR977809
    Digital Object Identifier: doi:10.1016/0168-0072(89)90005-5
    Zentralblatt MATH: 0628.03031
  • Ju. L. Ershov, A certain hierarchy of sets. I, Algebra i Logika, vol. 7 (1968), no. 1, pp. 47--74.
    Mathematical Reviews (MathSciNet): MR270911
  • --------, A certain hierarchy of sets. II, Algebra i Logika, vol. 7 (1968), no. 4, pp. 15--47.
    Mathematical Reviews (MathSciNet): MR270912
  • --------, A certain hierarchy of sets. III, Algebra i Logika, vol. 9 (1970), pp. 34--51.
    Mathematical Reviews (MathSciNet): MR299478
  • E. Mark Gold, Limiting recursion, Journal of Symbolic Logic, vol. 30 (1965), no. 1, pp. 28--48.
    Mathematical Reviews (MathSciNet): MR239972
    Digital Object Identifier: doi:10.2307/2270580
    Project Euclid: euclid.jsl/1183735041
    Zentralblatt MATH: 0203.01201
  • Hillary Putnam, Trial and error predicates and the solution to a problem of Mostowski, Journal of Symbolic Logic, vol. 30 (1965), no. 1, pp. 49--57.
    Mathematical Reviews (MathSciNet): MR195725
    Digital Object Identifier: doi:10.2307/2270581
    Project Euclid: euclid.jsl/1183735042
    Zentralblatt MATH: 0193.30102
  • Gerald E. Sacks, A minimal degree below $\textbf\upshape0'$, Bulletin of the American Mathematical Society, vol. 67 (1961), pp. 416--419.
    Mathematical Reviews (MathSciNet): MR126380
    Digital Object Identifier: doi:10.1090/S0002-9904-1961-10652-6
    Zentralblatt MATH: 0101.01202
  • --------, The recursively enumerable degrees are dense, Annals of Mathematics, vol. 80 (1964), pp. 300--312.
    Mathematical Reviews (MathSciNet): MR166089
    Digital Object Identifier: doi:10.2307/1970393
    JSTOR: links.jstor.org
  • Richard A. Shore and Theodore A. Slaman, Working below a high recursively enumerable degree, Journal of Symbolic Logic, vol. 58 (1993), no. 3, pp. 824--859.
    Mathematical Reviews (MathSciNet): MR1242041
    Digital Object Identifier: doi:10.2307/2275099
    Project Euclid: euclid.jsl/1183744300
    Zentralblatt MATH: 0797.03043
  • Theodore A. Slaman, The recursively enumerable degrees as a substructure of the $\Delta^0_2$-degrees, hand-written notes, 1983.
  • Robert I. Soare, Recursively enumerable sets and degrees, Springer--Verlag, Heidelberg, 1987.
    Mathematical Reviews (MathSciNet): MR882921
  • Yue Yang and Liang Yu, Elementary differences among finite levels of the Ershov hierarchy, Proceedings of TAMC2006: Theory and Applications of Models of Computation (Jin-Yi Cai, S. Barry Cooper, and Angsheng Li, editors), Lecture Notes in Computer Science, vol. 3959, Springer--Verlag, 2006, pp. 765--771.
    Mathematical Reviews (MathSciNet): MR2279139
    Digital Object Identifier: doi:10.1007/11750321_73
    Zentralblatt MATH: 1178.03053

Association for Symbolic Logic

Journal of Symbolic Logic
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more