Skip to main content Accessibility help
×
Home

Relative enumerability in the difference hierarchy

  • Marat M. Arslanov (a1), Geoffrey L. Laforte (a2) and Theodore A. Slaman (a3)

Abstract

We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.

Copyright

References

Hide All
[1]Arslanov, M. M., On the upper semilattice of Turing degrees below 0′, Soviet Mathematics, vol. 7 (1986), pp. 2733.
[2]Arslanov, M. M., Lempp, S., and Shore, R. A., Interpolating d.r.e. and RE A degrees between r.e. degrees, to appear in Annals of Pure and Applied Logic.
[3]Arslanov, M. M., On isolating r.e. and isolated d.r.e. degrees, Computability, enumerability, unsolvability (Cooper, S. B.et al., editors), London Mathematical Society Lecture Notes, no. 224, Cambridge University Press, 1996, pp. 6180.
[4]Cholak, P. and Hinman, P., Iterated relative recursive enumerability, Archive for Mathematical Logic, vol. 33 (1994), pp. 321346.
[5]Cooper, S. B., Lempp, S., and Watson, P., Weak density and cupping in the d.r.e. degrees, Israel Journal of Mathematics, vol. 67 (1989), pp. 137152.
[6]Cooper, S. B. and Yi, X., Isolated d.r.e. degrees, to appear, 1996.
[7]Ershov, Y. L., A hierarchy of sets, part I, Algebra and Logic, vol. 7 (1968), pp. 2443.
[8]Jockusch, C. and Shore, R., Pseudojump operators II: Transfinite iterations, hierarchies, and minimal covers, this Journal, vol. 49 (1984), pp. 12051236.
[9]Lachlan, A. H., Lower bounds for pairs of recursively enumerable degrees, Proceedings of the London Mathematical Society, vol. 16 (1966), pp. 537569.
[10]LaForte, G., Phenomena in the n-r.e. and n-REA degrees, Ph.D. thesis, University of Michigan, Ann Arbor, 1995.
[11]LaForte, G., The isolated d.r.e. degrees are dense in the r.e. degrees, Mathematical Logic Quarterly, vol. 42 (1996), no. 2.
[12]Putnam, H., Trial and error predicates and the solution to a problem of Mostowski, this Journal, vol. 30 (1965), pp. 4957.
[13]Soare, R. I., Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1987.
[14]Soare, R. I. and Stob, M., Relative recursive enumerability, Proceedings of the Herbrand symposium logic colloquium '81 (Stern, J., editor), North-Holland, Amsterdam, 1982, pp. 299324.

Related content

Powered by UNSILO

Relative enumerability in the difference hierarchy

  • Marat M. Arslanov (a1), Geoffrey L. Laforte (a2) and Theodore A. Slaman (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.