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Schnorr trivial sets and truth-table reducibility

Published online by Cambridge University Press:  12 March 2014

Johanna N. Y. Franklin  and
Frank Stephan
Johanna N. Y. Franklin
Affiliation:
Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, CanadaN2L 3G1 E-mail: jfranklin@math.uwaterloo.ca
Frank Stephan
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. Republic of Singapore. E-mail: fstephan@comp.nus.edu.sg
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 2 , June 2010 , pp. 501 - 521
Copyright
Copyright © Association for Symbolic Logic 2010

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