Splitting and jump inversion in the Turing degrees

S. Barry Cooper; Angsheng Li; Mingji Xia

doi:10.3233/COM-180083

Splitting and jump inversion in the Turing degrees

S. Barry Cooper
, Angsheng Li
, Mingji Xia

University of Leeds
Chinese Academy of Sciences

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

It is shown that for any computably enumerable degree a ‰ 0, and any Turing degree s, if s ≥ 0 ′, and c.e. in a, then there exists a c.e. degree x with the following properties: x < a, a is splittable over x, and x ′ = s.

源语言	英语
页（从-至）	133-142
页数	10
期刊	Computability
卷	7
期	2-3
DOI	https://doi.org/10.3233/COM-180083
出版状态	已出版 - 2018
已对外发布	是

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@article{d829fc770e2d44c986992d9efd12b1cf,

title = "Splitting and jump inversion in the Turing degrees",

abstract = "It is shown that for any computably enumerable degree a ‰ 0, and any Turing degree s, if s ≥ 0 ′, and c.e. in a, then there exists a c.e. degree x with the following properties: x < a, a is splittable over x, and x ′ = s.",

keywords = "Turing degrees, computably enumerable degree, jump inversion, splitting",

author = "Cooper, \{S. Barry\} and Angsheng Li and Mingji Xia",

year = "2018",

doi = "10.3233/COM-180083",

language = "英语",

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TY - JOUR

T1 - Splitting and jump inversion in the Turing degrees

AU - Cooper, S. Barry

AU - Li, Angsheng

AU - Xia, Mingji

PY - 2018

Y1 - 2018

N2 - It is shown that for any computably enumerable degree a ‰ 0, and any Turing degree s, if s ≥ 0 ′, and c.e. in a, then there exists a c.e. degree x with the following properties: x < a, a is splittable over x, and x ′ = s.

AB - It is shown that for any computably enumerable degree a ‰ 0, and any Turing degree s, if s ≥ 0 ′, and c.e. in a, then there exists a c.e. degree x with the following properties: x < a, a is splittable over x, and x ′ = s.

KW - Turing degrees

KW - computably enumerable degree

KW - jump inversion

KW - splitting

UR - https://www.scopus.com/pages/publications/85048720951

U2 - 10.3233/COM-180083

DO - 10.3233/COM-180083

M3 - 文章

AN - SCOPUS:85048720951

SN - 2211-3568

VL - 7

SP - 133

EP - 142

JO - Computability

JF - Computability

IS - 2-3

ER -

Splitting and jump inversion in the Turing degrees

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