A hierarchy for the plus cupping Turing degrees
Wang, Yong ; Li, Angsheng
J. Symbolic Logic, Tome 68 (2003) no. 1, p. 972- 988 / Harvested from Project Euclid
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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].
Publié le : 2003-09-14
Classification:  03D25,  03D30,  03D35 
@article{1058448450,
     author = {Wang, Yong and Li, Angsheng},
     title = {A hierarchy for the plus cupping Turing degrees},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 972- 988},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1058448450}
}

Wang, Yong; Li, Angsheng. A hierarchy for the plus cupping Turing degrees. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  972- 988. http://gdmltest.u-ga.fr/item/1058448450/