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May 2020 Effective Domination and the Bounded Jump
Keng Meng Ng, Hongyuan Yu
Notre Dame J. Formal Logic 61(2): 203-225 (May 2020). DOI: 10.1215/00294527-2020-0005

Abstract

We study the relationship between effective domination properties and the bounded jump. We answer two open questions about the bounded jump: (1) We prove that the analogue of Sacks jump inversion fails for the bounded jump and the wtt-reducibility. (2) We prove that no c.e. bounded high set can be low by showing that they all have to be Turing complete. We characterize the class of c.e. bounded high sets as being those sets computing the Halting problem via a reduction with use bounded by an ω-c.e. function. We define several notions of a c.e. set being effectively dominant, and show that together with the bounded high sets they form a proper hierarchy.

Citation

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Keng Meng Ng. Hongyuan Yu. "Effective Domination and the Bounded Jump." Notre Dame J. Formal Logic 61 (2) 203 - 225, May 2020. https://doi.org/10.1215/00294527-2020-0005

Information

Received: 13 February 2018; Accepted: 25 April 2019; Published: May 2020
First available in Project Euclid: 7 April 2020

zbMATH: 07222687
MathSciNet: MR4092531
Digital Object Identifier: 10.1215/00294527-2020-0005

Subjects:
Primary: 03D30
Secondary: 03D28

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 2 • May 2020
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