Principal filters definable by parameters in bt†

  • Authors:

  • Angsheng Li;Weilin Li;Yicheng Pan;Linqing Tang

  • Affiliations:

  • State key laboratory of computer science, and institute of software, chinese academy of sciences, p.o. box 8718, beijing, 100080, p.r. china email: angsheng@ios.ac.cn;State key laboratory of computer science, and institute of software, chinese academy of sciences, p.o. box 8718, beijing, 100080, p.r. china email: liweilin0919@gmail.com;State key laboratory of computer science, and institute of software, chinese academy of sciences, p.o. box 8718, beijing, 100080, p.r. china email: yicheng@ios.ac.cn;State key laboratory of computer science, and institute of software, chinese academy of sciences, p.o. box 8718, beijing, 100080, p.r. china email: tanglinqing05@mails.gucas.ac.cn and lingqing2001 ...

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2009

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Abstract

We show that there exist c.e. bounded Turing degrees a, b such that 0 a 0′, and that for any c.e. bounded Turing degree x, we have b ∨ x = 0′ if and only if x ≥ a. The result gives an unexpected definability theorem in the structure of bounded Turing reducibility.