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Degrees joining to 0

  • David B. Posner (a1) and Robert W. Robinson (a2)

It is shown that if and are sets of degrees uniformly recursive in 0′ with 0 then there is a degree b with b′ = 0′, bc = 0′ for every c, and ab for every a ˜ {0}. The proof is given as an oracle construction recursive in 0′. It follows that any nonrecursive degree below 0′ can be joined to 0′ by a degree strictly below 0′. Also, if a < 0′ and a″ = 0″ then there is a degree b such that ab = 0′ and ab = 0.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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