The low splitting theorem in the difference hierarchy

Angsheng Li

doi:10.1007/11494645_35

The low splitting theorem in the difference hierarchy

Angsheng Li^*

^*Corresponding author for this work

CAS - Institute of Software

Research output: Contribution to journal › Conference article › peer-review

3 Scopus citations

Abstract

It is shown that for any 2-computably enumerable Turing degrees a, l, if l′ = 0′, and l < a, then there are 2-computably enumerable Turing degrees x₀, x₁ such that both l ≤ x₀, x₁ < a and x₀ V x₁ = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.

Original language	English
Pages (from-to)	287-296
Number of pages	10
Journal	Lecture Notes in Computer Science
Volume	3526
DOIs	https://doi.org/10.1007/11494645_35
State	Published - 2005
Externally published	Yes
Event	First Conference on Computability in Europe, CiE 2005: New Computational Paradigms - Amsterdam, Netherlands Duration: 8 Jun 2005 → 12 Jun 2005

Access to Document

10.1007/11494645_35

Cite this

@article{7bffd3b81e1e478c81ac658fc10222eb,

title = "The low splitting theorem in the difference hierarchy",

abstract = "It is shown that for any 2-computably enumerable Turing degrees a, l, if l′ = 0′, and l < a, then there are 2-computably enumerable Turing degrees x0, x1 such that both l ≤ x0, x1 < a and x0 V x1 = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.",

author = "Angsheng Li",

year = "2005",

doi = "10.1007/11494645\_35",

language = "英语",

volume = "3526",

pages = "287--296",

journal = "Lecture Notes in Computer Science",

issn = "0302-9743",

publisher = "Springer Science and Business Media Deutschland GmbH",

note = "First Conference on Computability in Europe, CiE 2005: New Computational Paradigms ; Conference date: 08-06-2005 Through 12-06-2005",

}

TY - JOUR

T1 - The low splitting theorem in the difference hierarchy

AU - Li, Angsheng

PY - 2005

Y1 - 2005

N2 - It is shown that for any 2-computably enumerable Turing degrees a, l, if l′ = 0′, and l < a, then there are 2-computably enumerable Turing degrees x0, x1 such that both l ≤ x0, x1 < a and x0 V x1 = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.

AB - It is shown that for any 2-computably enumerable Turing degrees a, l, if l′ = 0′, and l < a, then there are 2-computably enumerable Turing degrees x0, x1 such that both l ≤ x0, x1 < a and x0 V x1 = a hold, extending the Robinson low splitting theorem for the computably enumerable degrees to the difference hierarchy.

UR - https://www.scopus.com/pages/publications/26444508964

U2 - 10.1007/11494645_35

DO - 10.1007/11494645_35

M3 - 会议文章

AN - SCOPUS:26444508964

SN - 0302-9743

VL - 3526

SP - 287

EP - 296

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - First Conference on Computability in Europe, CiE 2005: New Computational Paradigms

Y2 - 8 June 2005 through 12 June 2005

ER -

The low splitting theorem in the difference hierarchy

Abstract

Access to Document

Other files and links

Fingerprint

Cite this