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-bounding and -induction
Authors:Theodore A Slaman
Institution: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 $n\in\omega$, 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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