Schnorr triviality and genericity

Journal of Symbolic Logic 75 (1):191-207 (2010)

Abstract
We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of Schnorr trivial Turing degrees are precisely those whose jumps are at least 0"
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DOI 10.2178/jsl/1264433915
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References found in this work BETA

Calibrating Randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Classes of Recursively Enumerable Sets and Degrees of Unsolvability.Donald A. Martin - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):295-310.
Schnorr Trivial Reals: A Construction. [REVIEW]Johanna N. Y. Franklin - 2008 - Archive for Mathematical Logic 46 (7-8):665-678.

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Citations of this work BETA

On Effectively Closed Sets of Effective Strong Measure Zero.Kojiro Higuchi & Takayuki Kihara - 2014 - Annals of Pure and Applied Logic 165 (9):1445-1469.

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