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Jump operator and Yates Degrees

  • Guohua Wu (a1)

In [9], Yates proved the existence of a Turing degree a such that 0, 0′ are the only c.e. degrees comparable with it. By Slaman and Steel [7], every degree below 0′ has a 1-generic complement, and as a consequence, Yates degrees can be 1-generic, and hence can be low. In this paper, we prove that Yates degrees occur in every jump class.

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[4] G. E. Sacks , On the degrees less than 0(1), Annals of Mathematics, vol. 77 (1963), pp. 211231.

[8] R. I. Soare , Recursively enumerable sets and degrees, Springer-Verlag, Berlin, 1987.

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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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