Abstract
We shall show that if the theory S 02 of sharply bounded polynomial induction is extended by symbols for certain functions and their defining axioms, it is still far weaker than T 02 , which has ordinary sharply bounded induction. Furthermore, we show that this extended system S 02+ cannot ∑ b1 -define every function in AC 0, the class of functions computable by polynomial size constant depth circuits.
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© 1993 Springer-Verlag Berlin Heidelberg
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Johannsen, J. (1993). On the weakness of sharply bounded polynomial induction. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022571
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DOI: https://doi.org/10.1007/BFb0022571
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