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Every 1-generic computes a properly 1-generic

  • Barbara F. Csima (a1), Rod Downey (a2), Noam Greenberg (a3), Denis R. Hirschfeldt (a4) and Joseph S. Miller (a5)...
Abstract

A real is called properly n-generic if it is n-generic but not n + 1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.

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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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