Archive for Mathematical Logic 56 (5-6):507-521 (2017)

Anderson and Csima :245–264, 2014) defined a jump operator, the bounded jump, with respect to bounded Turing reducibility. They showed that the bounded jump is closely related to the Ershov hierarchy and that it satisfies an analogue of Shoenfield jump inversion. We show that there are high bounded low sets and low bounded high sets. Thus, the information coded in the bounded jump is quite different from that of the standard jump. We also consider whether the analogue of the Jump Theorem holds for the bounded jump: do we have A≤bTB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \le _{bT}B$$\end{document} if and only if Ab≤1Bb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^b \le _1 B^b$$\end{document}? We show the forward direction holds but not the reverse.
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DOI 10.1007/s00153-017-0537-8
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References found in this work BETA

A Refinement of Lown and Highn for the R.E. Degrees.Jeanleah Mohrherr - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (1-5):5-12.
A Bounded Jump for the Bounded Turing Degrees.Bernard Anderson & Barbara Csima - 2014 - Notre Dame Journal of Formal Logic 55 (2):245-264.

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Citations of this work BETA

Effective Domination and the Bounded Jump.Keng Meng Ng & Hongyuan Yu - 2020 - Notre Dame Journal of Formal Logic 61 (2):203-225.
Bounded-Low Sets and the High/Low Hierarchy.Huishan Wu - 2020 - Archive for Mathematical Logic 59 (7-8):925-938.

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