Article
On the Optimality of Conservation Results for Local Reflection in Arithmetic
Author/s | Cordón Franco, Andrés
![]() ![]() ![]() ![]() ![]() ![]() ![]() Fernández Margarit, Alejandro Lara Martín, Francisco Félix ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de Ciencias de la Computación e Inteligencia Artificial |
Publication Date | 2013 |
Deposit Date | 2021-04-09 |
Published in |
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Abstract | 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. |
Funding agencies | Ministerio de Ciencia e Innovación (MICIN). España |
Project ID. | MTM2008-06435
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Citation | 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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