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Adele Fernandez

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  •  Publications
    18
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Areas of Interest
Philosophy of Religion
17th/18th Century Philosophy
  • All publications (18)
  •  24
    Reseña "Hacia un ética ecológica, desde la interculturalidad" de Beatriz Sánchez Pirela
    Utopía y Praxis Latinoamericana 17 (58): 94-95. 2012.
  • Análisis no estándar y lógica
    Agora 12 (2): 163. 1993.
  • Introducción a las finanzas
    Civitas. forthcoming.
  •  37
    Reseña "Filosofía ¿para qué? Desafíos de la filosofía en el S. XXI" de Gabriel Vargas Lozano
    Utopía y Praxis Latinoamericana 18 (60): 133-135. 2013.
    Gilles Deleuze
  •  52
    Reseña "Tareas y Propuestas de la Filosofía Intercultural" de Raúl Fornet Betancourt
    Utopía y Praxis Latinoamericana 18 (60): 135-136. 2013.
  •  25
    Reseña "Retórica, democracia y crisis. Un estudio de teoría política" de Víctor Alonso Rocafort
    Utopía y Praxis Latinoamericana 17 (58): 99-100. 2012.
  •  25
    Reseña "La alternativa neopopulista" de Roberto Follari
    Utopía y Praxis Latinoamericana 17 (58): 100-101. 2012.
    German Philosophy
  •  62
    Reseña "El aprendizaje del aprendizaje" de Juan Ramón Capella
    Utopía y Praxis Latinoamericana 17 (58): 96-97. 2012.
  •  24
    Reseña "América. Recomienzo de la historia. La lectura auroral de la historia en la novela hispanoamericana" de Graciela Maturo
    Utopía y Praxis Latinoamericana 17 (58): 95-96. 2012.
  •  29
    Alejandro Moreno: Las epistemes del mundo-de-la-vida
    Utopía y Praxis Latinoamericana 14 (46): 5-6. 2009.
  •  55
    KAMENKA, EUGENE: De Philosophy of Ludwig Feuerbach
    Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 6 (6): 126-127. 1971.
    La idea de que la realidad, en múltiples de sus estratos, es un puro campo sobre el que recaen diversas interpretaciones plantea de inmediato la pregunta acerca de cuántas estrategias interpretativas generales son posibles respecto de la realidad y si estas estrategias, a las que denomino "políticas de la borrosidad", se aplican de una forma selectiva según los ámbitos de objetos de los que estemos hablando
    Continental Philosophy
  •  46
    Alberto Wagner de Reyna. In Memoriam (1915-2006)
    Utopía y Praxis Latinoamericana 11 (34): 0. 2006.
  •  39
    Induction, minimization and collection for Δ n+1 (T)–formulas
    with F. F. Lara-Martín
    Archive 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
    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 with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem
    Areas of Mathematics
  •  34
    On axiom schemes for T-provably $${\Delta_{1}}$$ Δ 1 formulas
    with A. Cordón-Franco and F. F. Lara-Martín
    Archive for Mathematical Logic 53 (3): 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 $${\Delta_1}$$ provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ implies $${B\Sigma_1}$$ to a purely recursion-theoretic question.
    Logic and Philosophy of Logic, Miscellaneous
  •  41
    On the quantifier complexity of Δ n+1 (T)– induction
    with A. Cordón-Franco and F. F. Lara-Martín
    Archive 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
    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, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2])
    Areas of Mathematics
  •  26
    On the Optimality of Conservation Results for Local Reflection in Arithmetic
    with A. Cordón-Franco and F. F. Lara-Martín
    Journal of Symbolic Logic 78 (4): 1025-1035. 2013.
    Logic and Philosophy of LogicLogic and Philosophy of Logic, Miscellaneous
  •  51
    A note on parameter free Π1 -induction and restricted exponentiation
    with A. Cordón-Franco and F. F. Lara-Martín
    Mathematical 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
    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, Weinheim
    Areas of Mathematics
  •  33
    Maximum Schemes in Arithmetic
    with M. J. Pérez-Jiménez
    Mathematical 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
    Theories of Mathematics, Misc
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