Notre Dame Journal of Formal Logic

Superhighness

Bjørn Kjos-Hanssen and Andrée Nies

Abstract

We prove that superhigh sets can be jump traceable, answering a question of Cole and Simpson. On the other hand, we show that such sets cannot be weakly 2-random. We also study the class $superhigh^\diamond$ and show that it contains some, but not all, of the noncomputable K-trivial sets.

Article information

Source
Notre Dame J. Formal Logic Volume 50, Number 4 (2009), 445-452.

Dates
First available in Project Euclid: 11 February 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1265899124

Digital Object Identifier
doi:10.1215/00294527-2009-020

Zentralblatt MATH identifier
05778810

Mathematical Reviews number (MathSciNet)
MR2598873

Subjects
Primary: 03D28
Secondary: 03D32 68Q30

Keywords
Turing degrees highness and lowness notions algorithmic randomness truth-table degrees

Citation

Kjos-Hanssen , Bjørn; Nies , Andrée. Superhighness. Notre Dame J. Formal Logic 50 (2009), no. 4, 445--452. doi:10.1215/00294527-2009-020. http://projecteuclid.org/euclid.ndjfl/1265899124.


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References

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