On the weakness of sharply bounded polynomial induction

  • Jan Johannsen
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 713)


We shall show that if the theory S 2 0 of sharply bounded polynomial induction is extended by symbols for certain functions and their defining axioms, it is still far weaker than T 2 0 , which has ordinary sharply bounded induction. Furthermore, we show that this extended system S 2+ 0 cannot ∑ 1 b -define every function in AC0, the class of functions computable by polynomial size constant depth circuits.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Jan Johannsen
    • 1
  1. 1.Friedrich-Alexander-Universität Erlangen-NürnbergGermany

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