Notre Dame Journal of Formal Logic

Effective Domination and the Bounded Jump

Keng Meng Ng and Hongyuan Yu

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 61, Number 2 (2020), 203-225.

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1586224879

Digital Object Identifier
doi:10.1215/00294527-2020-0005

Mathematical Reviews number (MathSciNet)
MR4092531

Zentralblatt MATH identifier
07222687

Subjects
Primary: 03D30: Other degrees and reducibilities
Secondary: 03D28: Other Turing degree structures

Keywords
wtt-degrees dominant function bounded jump jump inversion high degrees

Citation

Ng, Keng Meng; Yu, Hongyuan. Effective Domination and the Bounded Jump. Notre Dame J. Formal Logic 61 (2020), no. 2, 203--225. doi:10.1215/00294527-2020-0005. https://projecteuclid.org/euclid.ndjfl/1586224879


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