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March 2010 Schnorr triviality and genericity
Johanna N.Y. Franklin
J. Symbolic Logic 75(1): 191-207 (March 2010). DOI: 10.2178/jsl/1264433915

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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Johanna N.Y. Franklin. "Schnorr triviality and genericity." J. Symbolic Logic 75 (1) 191 - 207, March 2010. https://doi.org/10.2178/jsl/1264433915

Information

Published: March 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1184.03040
MathSciNet: MR2605888
Digital Object Identifier: 10.2178/jsl/1264433915

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 1 • March 2010
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