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A hierarchy for the plus cupping Turing degrees

  • Yong Wang (a1) and Angsheng Li (a2) (a3)

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 low n c. e. degree I such that xI = 0′. Let PC and PC n be the set of all plus-cupping, and n-plus-cupping c. e. degrees respectively. Then PC 1PC 2PC 3 = PC. In this paper we show that PC 1PC 2, so giving a nontrivial hierarchy for the plus cupping degrees. The theorem also extends the result of Li, Wu and Zhang [14] showing that LC 1LC 2, as well as extending the Harrington plus-cupping theorem [8].

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A hierarchy for the plus cupping Turing degrees

  • Yong Wang (a1) and Angsheng Li (a2) (a3)

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