Artículo
A note on parameter free Π1-induction and restricted exponentiation
Autor/es | Cordón Franco, Andrés
Fernández Margarit, Alejandro Lara Martín, Francisco Félix |
Departamento | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Fecha de publicación | 2011 |
Fecha de depósito | 2019-06-21 |
Publicado en |
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Resumen | 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 ... 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. |
Identificador del proyecto | MTM2005-08658
MTM2008-06435 |
Cita | 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. |
Ficheros | Tamaño | Formato | Ver | Descripción |
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A note on parameter free.pdf | 365.4Kb | [PDF] | Ver/ | |