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Parameter free induction and reflection

  • Lev D. Beklemishev
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1289)

Abstract

We give a precise characterization of parameter free Σn and IIn induction schemata, n and I II n , in terms of reflection principles. This allows us to show that I II n+1 is conservative over n w.r.t. boolean combinations of Σn+1 sentences, for n ≥ 1. In particular, we give a positive answer to a question by R. Kaye, whether the provably recursive functions of I II 2 are exactly the primitive recursive ones.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Lev D. Beklemishev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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