Complexity in Predicative Arithmetic

  • Geoffrey E. Ostrin
  • Stan S. Wainer
Conference paper

DOI: 10.1007/11494645_47

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)
Cite this paper as:
Ostrin G.E., Wainer S.S. (2005) Complexity in Predicative Arithmetic. In: Cooper S.B., Löwe B., Torenvliet L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg

Abstract

Complexity classes between Grzegorczyk’s E2 and E3 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.

Keywords

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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