\({\cal P}_w\) Is Not a Heyting Algebra

  • Kojiro Higuchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)


Let \({\cal P}_w\) denote the set of weak degrees of nonempty \(\Pi^0_1\) classes in the Cantor space 2 ω . We show that \({\cal P}_w\) is not a Heyting algebra. This is a solution to a question presented by Simpson [3].


\(\Pi^0_1\) classes weak reducibility Heyting algebras 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kojiro Higuchi
    • 1
  1. 1.Mathematical instituteTohoku UniversityMiyagiJapan

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