Journal of Symbolic Logic

Schnorr trivial sets and truth-table reducibility

Johanna N. Y. Franklin and Frank Stephan

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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.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 2 (2010), 501-521.

Dates
First available in Project Euclid: 18 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1268917492

Digital Object Identifier
doi:10.2178/jsl/1268917492

Mathematical Reviews number (MathSciNet)
MR2648153

Zentralblatt MATH identifier
1193.03073

Citation

Franklin, Johanna N. Y.; Stephan, Frank. Schnorr trivial sets and truth-table reducibility. J. Symbolic Logic 75 (2010), no. 2, 501--521. doi:10.2178/jsl/1268917492. https://projecteuclid.org/euclid.jsl/1268917492


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