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Hannah Höch: Notes on Violence and VulnerabilityIn Ruth Edith Hagengruber (ed.), Women Philosophers on Economics, Technology, Environment, and Gender History: Shaping the Future, Rethinking the Past, De Gruyter. pp. 271-282. 2023.
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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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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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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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13La crítica de Simone Weil a Marx: un referente para el pensamiento ecosocialistaIsegoría 66 27-27. 2022.In this article we discuss the political thought of the French philosopher Simone Weil. In particular, we analyse two fundamental elements of her critique of Marxism, namely her reflections on the phenomenon of power and her critique of the theory of the unlimited development of productive forces. We do so in dialogue with two of the pioneers of the ecosocialist critique of Marx in Spain: Manuel Sacristán and Francisco Fernández Buey, both readers of Weil. The aim: to point out the relevance of …Read more
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13From compassion to distance: Hannah Höch’s ‘Mother’European Journal of Women's Studies 29 (1): 140-154. 2022.This article addresses the work of the German artist Hannah Höch in the light of the struggle for abortion rights in the Weimar Republic. I attempt to show how Höch’s uses of the technique of photomontage can be read as a way of introducing a distance between the work and the viewer that allows us to question the beliefs we use to make sense of the world. Specifically, I discuss her photomontage Mutter, a version of a photograph taken by John Heartfield, and some of her writings and interviews. …Read more
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4Examinar críticamente la ciencia apelando a sus máximas, un reto feministaIsegoría 64 23-23. 2021.