Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 68, Issue 3 (2003), 972- 988.
A hierarchy for the plus cupping Turing degrees
We say that a computably enumerable (c. e.) degree a is plus-cupping, if for every c. e. degree x with 0 < x≤ a, there is a c. e. degree y ≠ 0’ such that x ∨ y=0’. We say that a is n-plus-cupping, if for every c. e. degree x, if 0 < x ≤ a, then there is a lown c. e. degree l such that x ∨ l=0’. Let PC and PCn be the set of all plus-cupping, and n-plus-cupping c. e. degrees respectively. Then PC1 ⊆ PC2⊆ PC3 = PC. In this paper we show that PC1 ⊂ PC2, 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 LC1 ⊂ LC2, as well as extending the Harrington plus-cupping theorem [harrington1978].
J. Symbolic Logic, Volume 68, Issue 3 (2003), 972- 988.
First available in Project Euclid: 17 July 2003
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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