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15Induction, 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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16On 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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17On 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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6On the Optimality of Conservation Results for Local Reflection in ArithmeticJournal of Symbolic Logic 78 (4): 1025-1035. 2013.
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28A 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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24Maximum 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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6Por Una Nueva Interpretación De La Teoría De Las IdeasEducação E Filosofia 25 (49): 227-239. 2011.El término phytourgo tiene importancia en el contexto de la naturaleza y la participación de las Ideas . Se aplica tanto al arte de imitar como a la producción de objetos por un artesano, además aparece en el contexto de generación de los seres vivos pero en ningún caso en la creación de las Ideas
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14Seifert, J.: "Conocimiento de Dios por las vías de la razón y del amor"Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 47 355-359. 2014.
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13Placebo Prescriptions Are Missed Opportunities for Doctor–Patient CommunicationAmerican Journal of Bioethics 9 (12): 48-50. 2009.
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La mónada pitagórica y el cosmos de PlatónOntology Studies: Cuadernos de Ontología 155-163. 2009.The interpretation of the platonic cosmogony presents one of its more controversial aspeects in the appreciation of the meaning of the creational act. The interpretations given so far clash with “creacionist” and the “mathematics” with passages that show the inadequacies of both approaches. Our work will analyse the different arguments concerning: 1) the status of the numbers; 2) the role of the limited, unlimited and the sperm; 3) the biological model of the platonic cosmology.La interpretación…Read more