Journal of Symbolic Logic

Limits on jump inversion for strong reducibilities

Barbara F. Csima, Rod Downey, and Keng Meng Ng

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 Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a Δ02 set B >tt ∅' such that there is no c.e. set A with A' ≡wtt B. We also show that there is a Σ02 set C >tt ∅' such that there is no Δ02 set D with D' ≡wtt C.

Article information

Source
J. Symbolic Logic Volume 76, Issue 4 (2011), 1287-1296.

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1318338849

Digital Object Identifier
doi:10.2178/jsl/1318338849

Zentralblatt MATH identifier
05991458

Mathematical Reviews number (MathSciNet)
MR2895396

Citation

Csima, Barbara F.; Downey, Rod; Ng, Keng Meng. Limits on jump inversion for strong reducibilities. Journal of Symbolic Logic 76 (2011), no. 4, 1287--1296. doi:10.2178/jsl/1318338849. http://projecteuclid.org/euclid.jsl/1318338849.


Export citation

References

  • B. Anderson, Automorhisms of the truth-table degrees are fixed on some cone, preprint, 2008.
  • S. Barry Cooper, Computability theory, Chapman & Hall/CRC, Boca Raton, FL, 2004.
  • O. Demuth, Remarks on the structure of tt-degrees based on constructive measure theory, Commentationes Mathematicae Universitatis Carolinae, vol. 29 (1988), no. 2, pp. 233–247.
  • R. Downey and J. Remmel, Classification of degree classes associated with r.e. subspaces, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 105–124.
  • R. Friedberg, A criterion for completeness of degrees of unsolvability, Journal of Symbolic Logic, vol. 22 (1958), pp. 159–160.
  • J. Mohrherr, Density of a final segment of the truth-table degrees, Pacific Journal of Mathematics, vol. 115 (1984), pp. 409–419.
  • E. Post, Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 284–316.
  • J. Reimann and T. Slaman, Measures and their random reals, preprint, 2008.
  • ––––, Probability measures and effective randomness, preprint, 2008.
  • R. Robinson, Jump restricted interpolation in the recursively enumerable degrees, Annals of Mathematics, vol. 93 (1971), no. 2, pp. 586–596.
  • G. Sacks, Recursive enumerability and the jump operator, 1963, vol. 108.
  • J. Shoenfield, On degrees of unsolvability, Annals of Mathematics, vol. 69 (1959), pp. 644–653.
  • R. Soare, Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, 1987.