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ON SUPERSETS OF NON-LOW$_2$ SETS

Part of: Computability and recursion theory

Published online by Cambridge University Press:  13 September 2021

KLAUS AMBOS-SPIES ,
ROD G. DOWNEY  and
MARTIN MONATH
KLAUS AMBOS-SPIES
Affiliation:
INSTITUT FÜR INFORMATIK UNIVERSITÄT HEIDELBERG IM NEUENHEIMER FELD 205 HEIDELBERGD-69120,GERMANYE-mail:ambos@math.uni-heidelberg.deE-mail:martin.monath@posteo.de
ROD G. DOWNEY
Affiliation:
SCHOOL OF MATHEMATICS AND STATISTICS VICTORIA UNIVERSITYWELLINGTON, P.O. BOX 600, NEW ZEALANDE-mail:rod.downey@vuw.ac.nz
MARTIN MONATH
Affiliation:
INSTITUT FÜR INFORMATIK UNIVERSITÄT HEIDELBERG IM NEUENHEIMER FELD 205 HEIDELBERGD-69120,GERMANYE-mail:ambos@math.uni-heidelberg.deE-mail:martin.monath@posteo.de
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Abstract

We solve a longstanding question of Soare by showing that if ${\mathbf d}$ is a non-low $_2$ computably enumerable degree then ${\mathbf d}$ contains a c.e. set with no r-maximal c.e. superset.

Keywords

computably enumerable setnon-low2r-maximal

MSC classification

Primary: 03D25: Recursively (computably) enumerable sets and degrees
Type
Article
Information
The Journal of Symbolic Logic , Volume 86 , Issue 3 , September 2021 , pp. 1282 - 1292
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Association for Symbolic Logic

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References

REFERENCES

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