Schnorr trivial sets and truth-table reducibility
Johanna N. Y. Franklin and Frank Stephan
Source: J. Symbolic Logic Volume 75, Issue 2
(2010), 501-521.
Abstract
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1268917492
Digital Object Identifier: doi:10.2178/jsl/1268917492
Zentralblatt MATH identifier: 05725861
Mathematical Reviews number (MathSciNet): MR2648153
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