Journal of Symbolic Logic

A hierarchy for the plus cupping Turing degrees

Angsheng Li and Yong Wang

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Abstract

We say that a computably enumerable (c. e.) degree a is plus-cupping, if for every c. e. degree x with 0 < xa, there is a c. e. degree y0’ such that xy=0’. We say that a is n-plus-cupping, if for every c. e. degree x, if 0 < xa, then there is a lown c. e. degree l such that xl=0’. Let PC and PCn be the set of all plus-cupping, and n-plus-cupping c. e. degrees respectively. Then PC1PC2PC3 = PC. In this paper we show that PC1PC2, so giving a nontrivial hierarchy for the plus cupping degrees. The theorem also extends the result of Li, Wu and Zhang [li-wu-zhang] showing that LC1LC2, as well as extending the Harrington plus-cupping theorem [harrington1978].

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 972- 988.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448450

Digital Object Identifier
doi:10.2178/jsl/1058448450

Mathematical Reviews number (MathSciNet)
MR2004f:03078

Zentralblatt MATH identifier
1061.03040

Subjects
Primary: 03D25: Recursively (computably) enumerable sets and degrees 03D30: Other degrees and reducibilities
Secondary: 03D35: Undecidability and degrees of sets of sentences

Citation

Wang, Yong; Li, Angsheng. A hierarchy for the plus cupping Turing degrees. J. Symbolic Logic 68 (2003), no. 3, 972-- 988. doi:10.2178/jsl/1058448450. https://projecteuclid.org/euclid.jsl/1058448450


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References

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