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-bounding and -induction
Authors:Theodore A. Slaman
Affiliation:Department of Mathematics, University of California Berkeley, Berkeley, California 94720-3840
Abstract:Working in the base theory of $mathrm{PA}^- + mathrm{I}Sigma_0 +exp$, we show that for all $ninomega$, the bounding principle for $Sigma_n$-formulas ( $mathrm{B}Sigma_n$) is equivalent to the induction principle for $Delta_n$-formulas ( $mathrm{I}Delta_n$). This partially answers a question of J. Paris.

Keywords:$Sigma_n$-bounding   $Delta_n$-induction
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