Francisco Martin

By a result of L.D. Beklemishev, the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over any $$\Pi _2$$ -axiomatizable base theory extending Elementary Arithmetic collapses to its first level. We prove that this result cannot in general be extended to base theories of arbitrary quantifier complexity. In fact, given any recursively enumerable set of true $$\Pi _2$$ -sentences, S, we construct a sound $$(\Sigma _2 \! \vee \! \Pi _2)$$ -axiomatized theory T extending S such that the hierarchy of nested applications of the $$\Sigma _1$$ -collection rule over T is proper. Our construction uses some results on subrecursive degree theory obtained by L. Kristiansen.

In this article Jason Brennan’s arguments about the moral duties relating to our practice of voting are examined. These arguments provide an epistocratic approach of politics and present a conception of abstention at four levels: abstention as a personal choice, as a moral responsibility, as a duty legally enforceable and as an obligation decided by lot. The contrast with John Stuart Mill’s positions helps to highlight the postdemocratic ambivalences and the latent paternalism behind Brennan’s rejection of massive voting and electoral democracy. A deliberative, Millian-inspired understanding of abstention also allows questioning the assumption in Brennan’s successive proposals that there is no significant loss in overlooking the political valence of qualified abstention.

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

El siguiente informe pericial se basa en la experiencia de investigación de los firmantes en relación a las exhumaciones de fosas comunes de la Guerra Civil y la postguerra, y al conocido como “movimiento para la recuperación de la memoria histórica” que están teniendo lugar en España desde el año 2000, que ha enfatizado sus demandas sobre la suerte de los desaparecidos y ha puesto en marcha un ciclo de exhumaciones de fosas comunes derivadas de la Guerra Civil y la dictadura. En este peritaje se usan las exhumaciones del siglo XXI como indicadores de la persistencia en el tiempo de las políticas y culturas del miedo instaladas en la sociedad española durante la Guerra Civil y la dictadura, más allá de las profundas transformaciones políticas e institucionales acaecidas en el país tras la muerte de Francisco Franco. Fue presentado como parte de la documentación de la demanda de Fausto Canales contra España el 15 de septiembre de 2012 en el Tribunal Europeo de Derechos Humanos.

In this paper we argue that the best way to explain the normative framework of science is to adopt a model inspired in the democratic characterization of a public sphere. This model assumes and develops some deliberative democratic principles about the inclusiveness of the concerned, the parity of the reasons and the general interest of the subjects. In contrast to both bargaining models and to power-inspired models of the scientific activities, the model of scientific public sphere proposes to account for the self-legislative capacity of science, the public nature of the scientific results and the epistemic virtues of scientific research in terms of the deliberative process carried out by individuals who are engaging in the public use of reason. This perspective provides new insights into the normative conditions of a democratic science.

Let T be a second-order arithmetical theory, Λ a well-order, λ < Λ and X ⊆ ℕ. We use $[\lambda |X]_T^{\rm{\Lambda }}\varphi$ as a formalization of “φ is provable from T and an oracle for the set X, using ω-rules of nesting depth at most λ”.For a set of formulas Γ, define predicative oracle reflection for T over Γ ) to be the schema that asserts that, if X ⊆ ℕ, Λ is a well-order and φ ∈ Γ, then$$\forall \,\lambda < {\rm{\Lambda }}\,.$$In particular, define predicative oracle consistency ) as Pred–O–RFN{0=1}.Our main result is as follows. Let ATR0 be the second-order theory of Arithmetical Transfinite Recursion, ${\rm{RCA}}_0^{\rm{*}}$ be Weakened Recursive Comprehension and ACA be Arithmetical Comprehension with Full Induction. Then,$${\rm{ATR}}_0 \equiv {\rm{RCA}}_0^{\rm{*}} + {\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - Cons\ }}\left \equiv {\rm{RCA}}_0^{\rm{*}} + \,{\rm{Pred - O - RFN}}\,_{{\bf{\Pi }}_2^1 } \left.$$We may even replace ${\rm{RCA}}_0^{\rm{*}}$ by the weaker ECA0, the second-order analogue of Elementary Arithmetic.Thus we characterize ATR0, a theory often considered to embody Predicative Reductionism, in terms of strong reflection and consistency principles.

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 provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether IΔ0+¬exp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${I\Delta_0 + \neg \mathit{exp}}$$\end{document} implies BΣ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B\Sigma_1}$$\end{document} to a purely recursion-theoretic question.

Let Iπ2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free Π2Π2 formulas. Answering a question of R. Kaye, L. Beklemishev showed that the provably total computable functions of Iπ2 are, precisely, the primitive recursive ones. In this work we give a new proof of this fact through an analysis of certain local variants of induction principles closely related to Iπ2. In this way, we obtain a more direct answer to Kaye's question, avoiding the metamathematical machinery needed for Beklemishev's original proof.Our methods are model-theoretic and allow for a general study of Iπn+1 for all n≥0n≥0. In particular, we derive a new conservation result for these theories, namely that Iπn+1 is πn+2 -conservative over IΣn for each n≥1n≥1.

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])

En esta investigación intentaremos explicitar hasta qué punto Ser y Tiempo es una suerte de tentativa por retomar, en forma correcta, el originario proyecto filosófico que Kant desplegó en su Crítica de la razón pura. Para lograr justificar nuestra conjetura nos centraremos especialmente en la obra de Heidegger Kant y el problema de la Metafísica (1929). En dicho texto nos encontraremos con una controvertida interpretación que el pensador de Meßkirch elaboró del opus magnum de Immanuel Kant. Interpretación que, justamente, podría sugerirnos que su Ser y Tiempo, no sólo estaría hermanado con la Crítica de la razón pura, sino que vendría a ser una correcta continuación del camino allí trazado por el filósofo de Königsberg.

Este artículo aborda la aplicación de la técnica del andamiaje en un proceso de evaluación a nivel de máster universitario. En el ámbito de la comunicación digital, se propuso al alumnado la realización de una campaña para un cliente real, una asociación protectora de animales. A través de la técnica de la observación participante y de una encuesta al alumnado, se llevó a cabo este proyecto cuyos resultados muestran que el andamiaje es efectivo en el nivel de máster y que su combinación con la tecnología y la motivación del profesorado contribuye a obtener mejores resultados.

En este artículo se analizan algunas de las implicaciones que tienen las prácticas de triaje para la ética de desastres. Se considera la centralidad técnica de la cuantificación en los modelos algorítmicos y numéricos de triaje y se incide en la prevalencia normativa de los criterios consecuencialistas, incluso cuando éstos hayan de ajustarse a sistemas de múltiples principios. Finalmente se sugiere que una concepción ética de los desastres precisa de una perspectiva compleja y integral de la gestión de los desastres que no se limite a la fase de respuesta inmediata a los mismos y que supere a la par que integre los principios de la bioética y la indispensabilidad de los criterios consecuencialistas en las decisiones de triaje.

La presente investigación tiene por objeto explicitar, dentro de una posible y sugestiva interpretación, los motivos por los cuales Aristóteles comprendió la necesidad de postular la vía final como camino para efectuar eficientemente la Filosofía Primera. Así lo anterior, revisaremos su crítica de las causas empleadas por su tradición filosófica: la material, la eficiente y la formal. Finalmente, halladas las razones que auspician la necesidad de postular una cuarta causa, la final, presentaremos los puntos cardinales de su lógoi Θ en tanto conclusión del fundador del Liceo con respecto a su Filosofía Primera: la Ontología modal.

The aim of this article is to map the intellectual structure of scholarship on economic and social value in the sport industry. Given that bibliometric techniques are specially appropriate for identifying the intellectual structures of a field of knowledge and complement traditional literature reviews, a co-citation bibliometric analysis has been applied. This kind of analysis identifies networks of interconnections. Therefore, we aim to detect both the most and the least active research areas in this field, as well as their sub-disciplinary composition. There is an abundance of literature on sport efficiency and economic efficiency in the sport industry, our main conclusion is the identification of a literature gap in regard to social value in sport organisations, which is expected to be a research opportunity for scholars. This is in line with the lack of standardisation in the measurement for social value in sport organisations. In fact, similar to analysis undertaken in the past few decades of other industries with contributions to stakeholders and the multi-fiduciary theory of stakeholders, both the creation of social value indicators for sport entities and the empirical analysis of social efficiency in sport institutions, are identified and outlined as future areas of research. Therefore, this bibliometric analysis will contribute to determine the future challenges that this area of research will face in the following years so as to fill the literature gap identified.

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