There is no low maximal d. c. e. degree

Marat Arslanov; S. Barry Cooper; Angsheng Li

doi:10.1002/1521-3870(200008)46:3<409::AID-MALQ409>3.0.CO;2-P

There is no low maximal d. c. e. degree

Marat Arslanov^*
, S. Barry Cooper
, Angsheng Li

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We show that for any computably enumerable (c. e.) set A and any Δ⁰₂ set L, if L is low and L <_T A, then there is a c. e. splitting A₀ ∐ A₁ = A such that A_i ⊗ L <_T A. In particular, if L is low and n-c. e., then A_i ⊗ L is n-c. e. and hence there is no low maximal n-c. e. degree.

Original language	English
Pages (from-to)	409-416
Number of pages	8
Journal	Mathematical Logic Quarterly
Volume	46
Issue number	3
DOIs	https://doi.org/10.1002/1521-3870(200008)46:3<409::AID-MALQ409>3.0.CO;2-P
State	Published - 2000
Externally published	Yes

Keywords

Computably enumerable set
Maximal d. c. e. degree
N-c.E. set

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10.1002/1521-3870(200008)46:3<409::AID-MALQ409>3.0.CO;2-P

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title = "There is no low maximal d. c. e. degree",

abstract = "We show that for any computably enumerable (c. e.) set A and any Δ02 set L, if L is low and L <T A, then there is a c. e. splitting A0 ∐ A1 = A such that Ai ⊗ L <T A. In particular, if L is low and n-c. e., then Ai ⊗ L is n-c. e. and hence there is no low maximal n-c. e. degree.",

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T1 - There is no low maximal d. c. e. degree

AU - Arslanov, Marat

AU - Cooper, S. Barry

AU - Li, Angsheng

PY - 2000

Y1 - 2000

N2 - We show that for any computably enumerable (c. e.) set A and any Δ02 set L, if L is low and L <T A, then there is a c. e. splitting A0 ∐ A1 = A such that Ai ⊗ L <T A. In particular, if L is low and n-c. e., then Ai ⊗ L is n-c. e. and hence there is no low maximal n-c. e. degree.

AB - We show that for any computably enumerable (c. e.) set A and any Δ02 set L, if L is low and L <T A, then there is a c. e. splitting A0 ∐ A1 = A such that Ai ⊗ L <T A. In particular, if L is low and n-c. e., then Ai ⊗ L is n-c. e. and hence there is no low maximal n-c. e. degree.

KW - Computably enumerable set

KW - Maximal d. c. e. degree

KW - N-c.E. set

UR - https://www.scopus.com/pages/publications/0034344093

U2 - 10.1002/1521-3870(200008)46:3<409::AID-MALQ409>3.0.CO;2-P

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SN - 0942-5616

VL - 46

SP - 409

EP - 416

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 3

ER -

There is no low maximal d. c. e. degree

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Keywords

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