Chapter

New Computational Paradigms

Volume 3526 of the series Lecture Notes in Computer Science pp 378-384

Complexity in Predicative Arithmetic

  • Geoffrey E. OstrinAffiliated withInstitut für Informatik und angewandte Mathematik
  • , Stan S. WainerAffiliated withDepartment of Pure Mathematics, University of Leeds

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Abstract

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.

Keywords

provable recursion ordinal analysis slow growing hierarchy