Journal of Symbolic Logic

Schnorr trivial sets and truth-table reducibility

Johanna N. Y. Franklin and Frank Stephan

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

First available in Project Euclid: 18 March 2010

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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.

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