Complexity in Predicative Arithmetic
- 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
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.
Keywordsprovable recursion ordinal analysis slow growing hierarchy
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