A join theorem for the computably enumerable degrees

Carl G. Jockusch; Angsheng Li; Yue Yang

doi:10.1090/S0002-9947-04-03585-8

A join theorem for the computably enumerable degrees

Carl G. Jockusch^*
, Angsheng Li
, Yue Yang

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

8 引用（Scopus）

摘要

It is shown that for any computably enumerable (c.e.) degree w, if w ≠ 0, then there is a c.e. degree a such that (a ∨ w)′ = a″ = 0″ (so a is low ₂ and a ∨ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low ₂ c.e. degrees are not elementarily equivalent as partial orderings.

源语言	英语
页（从-至）	2557-2568
页数	12
期刊	Transactions of the American Mathematical Society
卷	356
期	7
DOI	https://doi.org/10.1090/S0002-9947-04-03585-8
出版状态	已出版 - 7月 2004
已对外发布	是

访问文件

10.1090/S0002-9947-04-03585-8

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{df3b5dcae7b04c55b66a6ab65bdf13e4,

title = "A join theorem for the computably enumerable degrees",

abstract = "It is shown that for any computably enumerable (c.e.) degree w, if w ≠ 0, then there is a c.e. degree a such that (a ∨ w)′ = a″ = 0″ (so a is low 2 and a ∨ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low 2 c.e. degrees are not elementarily equivalent as partial orderings.",

keywords = "Computably enumerable degree, Definable ideals, Join theorem, Turing jump",

author = "Jockusch, \{Carl G.\} and Angsheng Li and Yue Yang",

year = "2004",

month = jul,

doi = "10.1090/S0002-9947-04-03585-8",

language = "英语",

volume = "356",

pages = "2557--2568",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "7",

}

TY - JOUR

T1 - A join theorem for the computably enumerable degrees

AU - Jockusch, Carl G.

AU - Li, Angsheng

AU - Yang, Yue

PY - 2004/7

Y1 - 2004/7

N2 - It is shown that for any computably enumerable (c.e.) degree w, if w ≠ 0, then there is a c.e. degree a such that (a ∨ w)′ = a″ = 0″ (so a is low 2 and a ∨ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low 2 c.e. degrees are not elementarily equivalent as partial orderings.

AB - It is shown that for any computably enumerable (c.e.) degree w, if w ≠ 0, then there is a c.e. degree a such that (a ∨ w)′ = a″ = 0″ (so a is low 2 and a ∨ w is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low 2 c.e. degrees are not elementarily equivalent as partial orderings.

KW - Computably enumerable degree

KW - Definable ideals

KW - Join theorem

KW - Turing jump

UR - https://www.scopus.com/pages/publications/2942644633

U2 - 10.1090/S0002-9947-04-03585-8

DO - 10.1090/S0002-9947-04-03585-8

M3 - 文章

AN - SCOPUS:2942644633

SN - 0002-9947

VL - 356

SP - 2557

EP - 2568

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 7

ER -

A join theorem for the computably enumerable degrees

摘要

访问文件

其它文件与链接

指纹

引用此