Cordón Franco, AndrésFernández Margarit, AlejandroLara Martín, Francisco Félix2019-06-212019-06-212011Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2011). A note on parameter free Π1-induction and restricted exponentiation. Mathematical Logic Quaterly, 57 (5), 444-455.0942-5616https://hdl.handle.net/11441/87541We characterize the sets of all Π2 and all $\mathcal {B}(\Sigma _{1})$equation image (= Boolean combinations of Σ1) theorems of IΠ−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 IΠ−n + 1 is conservative over IΣ−n with respect to $\mathcal {B}(\Sigma _{n+1})$equation image sentences cannot be extended to Πn + 2 sentences.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/First order arithmeticParameter free inductionExponentiationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1002/malq.201010013