Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 55, Number 2 (2014), 245-264.
A Bounded Jump for the Bounded Turing Degrees
We define the bounded jump of by and let denote the th bounded jump. We demonstrate several properties of the bounded jump, including the fact that it is strictly increasing and order-preserving on the bounded Turing () degrees (also known as the weak truth-table degrees). We show that the bounded jump is related to the Ershov hierarchy. Indeed, for we have is -c.e. , extending the classical result that is -c.e. Finally, we prove that the analogue of Shoenfield inversion holds for the bounded jump on the bounded Turing degrees. That is, for every such that , there is a such that .
Notre Dame J. Formal Logic, Volume 55, Number 2 (2014), 245-264.
First available in Project Euclid: 24 April 2014
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Primary: 03D30: Other degrees and reducibilities
Anderson, Bernard; Csima, Barbara. A Bounded Jump for the Bounded Turing Degrees. Notre Dame J. Formal Logic 55 (2014), no. 2, 245--264. doi:10.1215/00294527-2420660. https://projecteuclid.org/euclid.ndjfl/1398345783