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There is No Low Maximal D.C.E. Degree
Author(s) -
Arslanov Marat,
Cooper S. Barry,
Li Angsheng
Publication year - 2000
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200008)46:3<409::aid-malq409>3.0.co;2-p
Subject(s) - mathematics , degree (music) , combinatorics , set (abstract data type) , discrete mathematics , physics , computer science , acoustics , programming language
We show that for any computably enumerable (c.e.) set A and any $\Delta ^0_2$ set L , if L is low and $L <_{\rm T} A$ , then there is a c.e. splitting $A_0 \sqcup A_1 = A$ such that $A_i \oplus L <_{\rm T} A$ . In Particular, if L is low and n ‐c.e., then $A_i \oplus L$ is n ‐c.e. and hence there is no low maximal n ‐c.e. degree.