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- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer-Verlag
- Subject
- Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-010-0187-6
- Publisher site
- See Article on Publisher Site
Abstract
A Schnorr test relative to some oracle A may informally be called “universal” if it covers all Schnorr tests. Since no true universal Schnorr test exists, such an A cannot be computable. We prove that the sets with this property are exactly those with high Turing degree. Our method is closely related to the proof of Terwijn and Zambella’s characterization of the oracles which are low for Schnorr tests. We also consider the oracles which compute relativized Schnorr tests with the weaker property of covering all computable reals. The degrees of these oracles strictly include the hyperimmune degrees and are strictly included in the degrees not computably traceable.
Journal
Archive for Mathematical Logic – Springer Journals
Published: May 12, 2010