On the weakness of sharply bounded polynomial induction
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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