Schnorr trivial sets and truth-table reducibility

@article{Franklin2010SchnorrTS,
  title={Schnorr trivial sets and truth-table reducibility},
  author={Johanna N. Y. Franklin and Frank Stephan},
  journal={J. Symb. Log.},
  year={2010},
  volume={75},
  pages={501-521}
}
We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte. 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 22 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 28 references

The degrees of hyperimmune sets

  • Webb Miller, Donald Martin
  • Zeitschrift für Mathematische Logik und…
  • 1968
Highly Influential
14 Excerpts

Aspects of Schnorr randomness

  • Johanna N.Y. Franklin
  • Ph.D. dissertation, University of California…
  • 2007
Highly Influential
8 Excerpts

Classical Recursion Theory, Volume II

  • Piergiorgio Odifreddi
  • 1999
Highly Influential
3 Excerpts

Algorithmic Randomness

  • Nenad Mihailović
  • 2007

Algorithmic Randomness. Inaugural-Dissertation

  • Nenad Mihailović
  • University of Heidelberg,
  • 2007

Similar Papers

Loading similar papers…