Schnorr trivial sets and truth-table reducibility

Journal of Symbolic Logic 75 (2):501-521 (2010)
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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DOI 10.2178/jsl/1268917492
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Webb Miller & D. A. Martin (1968). The Degrees of Hyperimmune Sets. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 14 (7-12):159-166.
Webb Miller & D. A. Martin (1968). The Degrees of Hyperimmune Sets. Mathematical Logic Quarterly 14 (7‐12):159-166.

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