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2014 A Bounded Jump for the Bounded Turing Degrees
Bernard Anderson, Barbara Csima
Notre Dame J. Formal Logic 55(2): 245-264 (2014). DOI: 10.1215/00294527-2420660

Abstract

We define the bounded jump of A by Ab={xωix[φi(x)ΦxAφi(x)(x)]} and let Anb denote the nth 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 (bT) degrees (also known as the weak truth-table degrees). We show that the bounded jump is related to the Ershov hierarchy. Indeed, for n2 we have XbTnbX is ωn-c.e. X1nb, extending the classical result that XbT'X is ω-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 X such that bbTXbT2b, there is a YbTb such that YbbTX.

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Bernard Anderson. Barbara Csima. "A Bounded Jump for the Bounded Turing Degrees." Notre Dame J. Formal Logic 55 (2) 245 - 264, 2014. https://doi.org/10.1215/00294527-2420660

Information

Published: 2014
First available in Project Euclid: 24 April 2014

zbMATH: 1307.03024
MathSciNet: MR3201835
Digital Object Identifier: 10.1215/00294527-2420660

Subjects:
Primary: 03D30

Keywords: $bT$-degrees , bounded jump , bounded Turing degrees , jump , wtt degrees

Rights: Copyright © 2014 University of Notre Dame

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Vol.55 • No. 2 • 2014
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