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A note on parameter free Π1-induction and restricted exponentiation

A note on parameter free Π1-induction and restricted exponentiation
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 Author: Cordón Franco, Andrés Fernández Margarit, Alejandro Lara Martín, Francisco Félix Department: Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial Date: 2011 Published in: Mathematical Logic Quaterly, 57 (5), 444-455. Document type: Article Abstract: We 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. Cite: Cordón 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.
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DOI: 10.1002/malq.201010013

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