Schnorr triviality and genericity
Johanna N.Y. Franklin
Source: J. Symbolic Logic Volume 75, Issue 1
(2010), 191-207.
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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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1264433915
Digital Object Identifier: doi:10.2178/jsl/1264433915
Zentralblatt MATH identifier: 05681298
Mathematical Reviews number (MathSciNet): MR2605888
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