论文信息 - A hierarchy for the plus cupping Turing degrees

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 V 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 I such that x vI = 0'. Let PC and PCn be the set of all plus-cupping, and n-plus-cupping c. e. degrees respectively. Then PC1 C PC2 C PC3 = PC. In this paper we show that PCI C PC2, so giving a nontrivial hierarchy for the plus cupping degrees. The theorem also extends the result of Li, Wu and Zhang [14] showing that LCI C LC2, as well as extending the Harrington plus-cupping theorem [8]. ?

Yong Wang | Angsheng Li | Angsheng Li | Yong Wang

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