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19On the quantifier complexity of Δ n+1 (T)– inductionArchive for Mathematical Logic 43 (3): 371-398. 2004.In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction rule for Δ n+1 –formulas. Our arguments, invo…Read more
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26Maximum Schemes in ArithmeticMathematical Logic Quarterly 40 (3): 425-430. 1994.In this paper we deal with some new axiom schemes for Peano's Arithmetic that can substitute the classical induction, least-element, collection and strong collection schemes in the description of PA
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21Induction, minimization and collection for Δ n+1 (T)–formulasArchive for Mathematical Logic 43 (4): 505-541. 2004.For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected …Read more
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17On axiom schemes for T-provably $${\Delta_{1}}$$ Δ 1 formulasArchive for Mathematical Logic 53 (3-4): 327-349. 2014.This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are Δ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta_1}$$\end{document} provably in an arithmetic theory T. In particular, we determine the pr…Read more
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8On the Optimality of Conservation Results for Local Reflection in ArithmeticJournal of Symbolic Logic 78 (4): 1025-1035. 2013.
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33A note on parameter free Π1 -induction and restricted exponentiationMathematical Logic Quarterly 57 (5): 444-455. 2011.We characterize the sets of all Π2 and all equation image 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 equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, We…Read more
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17Reseña "Hacia un ética ecológica, desde la interculturalidad" de Beatriz Sánchez PirelaUtopía y Praxis Latinoamericana 17 (58): 94-95. 2012.
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15Reseña "América. Recomienzo de la historia. La lectura auroral de la historia en la novela hispanoamericana" de Graciela MaturoUtopía y Praxis Latinoamericana 17 (58): 95-96. 2012.
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49Reseña "El aprendizaje del aprendizaje" de Juan Ramón CapellaUtopía y Praxis Latinoamericana 17 (58): 96-97. 2012.
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35Reseña "Tareas y Propuestas de la Filosofía Intercultural" de Raúl Fornet BetancourtUtopía y Praxis Latinoamericana 18 (60): 135-136. 2013.
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11Reseña "La alternativa neopopulista" de Roberto FollariUtopía y Praxis Latinoamericana 17 (58): 100-101. 2012.
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13Reseña "Retórica, democracia y crisis. Un estudio de teoría política" de Víctor Alonso RocafortUtopía y Praxis Latinoamericana 17 (58): 99-100. 2012.
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134Truths will be defined as an agreement on uncertainties, the consensus over matters of empirical and social nature such as mathematics, physics or economics. As illustrated by Dennis Lindley , ‘individuals tend to know things to be true and false but the extent of this truth and falsity would always remain unknown’. Leading individuals to a permanent state of stress, uncertainty becomes a risk for the social community. Problems could not be presumed to be solvable as any kind of solution would…Read more
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Universidad Autónoma de MadridGraduate student
Areas of Interest
Normative Ethics |
Philosophy of Law |
Social and Political Philosophy |
European Philosophy |