A note on parameter free ?1-induction and restricted exponentiation
We characterize the sets of all ?2 and all (= Boolean combinations of ?1) theorems of I??1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that I??n + 1 is conservative over I??n with respect to sentences cannot be extended to ?n + 2 sentences.  2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
first order arithmetic parameter free induction exponentiation. msc (2010) 03f30 03h15