Complexity in Predicative Arithmetic

  • Geoffrey E. Ostrin
  • Stan S. Wainer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)


Complexity classes between Grzegorczyk’s E 2 and E 3 are characterized in terms of provable recursion in a theory EA(I;O) formalising basic principles of Nelson’s Predicative Arithmetic. Extensions by inductive definitions enable full arithmetic PA and higher systems to be recaptured in a setting where the natural bounding functions are “slow” rather than “fast” growing.


provable recursion ordinal analysis slow growing hierarchy 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Geoffrey E. Ostrin
    • 1
  • Stan S. Wainer
    • 2
  1. 1.Institut für Informatik und angewandte MathematikBernSwitzerland
  2. 2.Department of Pure MathematicsUniversity of LeedsLeedsUK

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