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Principal filters definable by parameters in 𝓔bT†

Published online by Cambridge University Press:  01 February 2009

ANGSHENG LI ,
WEILIN LI ,
YICHENG PAN  and
LINQING TANG
ANGSHENG LI
Affiliation:
State Key Laboratory of Computer Science, and Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, Beijing, 100080, P.R. China Email: angsheng@ios.ac.cn
WEILIN LI
Affiliation:
State Key Laboratory of Computer Science, and Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, Beijing, 100080, P.R. China Email: liweilin0919@gmail.com
YICHENG PAN
Affiliation:
State Key Laboratory of Computer Science, and Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, Beijing, 100080, P.R. China Email: yicheng@ios.ac.cn
LINQING TANG
Affiliation:
State Key Laboratory of Computer Science, and Institute of Software, Chinese Academy of Sciences, P.O. Box 8718, Beijing, 100080, P.R. China Email: tanglinqing05@mails.gucas.ac.cn and lingqing2001@163.com
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Abstract

We show that there exist c.e. bounded Turing degrees a, b such that 0 < a < 0′, and that for any c.e. bounded Turing degree x, we have b ∨ x = 0′ if and only if x ≥ a. The result gives an unexpected definability theorem in the structure of bounded Turing reducibility.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 19 , Special Issue 1: Theory and Applications of Models of Computation (TAMC) , February 2009 , pp. 153 - 167
Copyright
Copyright © Cambridge University Press 2009

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