Artículo
On the Optimality of Conservation Results for Local Reflection in Arithmetic
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 | 2013 |
Fecha de depósito | 2021-04-09 |
Publicado en |
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Resumen | Let T be a recursively enumerable theory extending Elementary Arithmetic EA. L. D. Beklemishev proved that the Σ2 local reflection principle for T, (T), is conservative over the Σ1 local reflection principle, (T), with ... Let T be a recursively enumerable theory extending Elementary Arithmetic EA. L. D. Beklemishev proved that the Σ2 local reflection principle for T, (T), is conservative over the Σ1 local reflection principle, (T), with respect to boolean combinations of Σ1-sentences; and asked whether this result is best possible. In this work we answer Beklemishev's question by showing that Π2-sentences are not conserved for T = EA + “f is total,” where f is any nondecreasing computable function with elementary graph. We also discuss how this result generalizes to n > 0 and obtain as an application that for n > 0, is conservative over IΣ n with respect to Π n+2-sentences. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España |
Identificador del proyecto | MTM2008-06435 |
Cita | Cordón Franco, A., Fernández Margarit, A. y Lara Martín, F.F. (2013). On the Optimality of Conservation Results for Local Reflection in Arithmetic. The Journal of Symbolic Logic, 78 (4), 1025-1035. |
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