Induction, minimization and collection for Δ n+1 (T)–formulas

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.Ministerio de Educación y Cultura DGES PB96-134

Fauteuil roulante eléctrique

Reemplazar el joystick de una silla de ruedas eléctrica por un dispositivo que se adapte a las capacidades de niños poli discapacitados.Desarrollar una interfaz que muestre los movimientos de la silla de ruedas para hacer posible el aprendizaje de los niños.Departamento de Ciencias de los Materiales e Ingeniería Metalúrgica, Expresión Gráfica en la Ingeniería, Ingeniería Cartográfica, Geodesia y Fotogrametría, Ingeniería Mecánica e Ingeniería de los Procesos de FabricaciónGrado en Ingeniería Mecánic

La cultura en la comunidad iberoamericana de naciones: la necesaria instauración de un entramado jurídico [book review]

Este artículo reseña: Cástor Díaz Barrado. La cultura en la comunidad iberoamericana de naciones: la necesaria instauración de un entramado jurídico. Plaza y Valdés, Madrid, 320 pp

Formación profesional reglada para mujeres y hombres inmigrantes : el caso de la ciudad de Granada

El artículo expone los resultados de un trabajo centrado en el análisis de la formación profesional reglada en un contexto local preciso, la ciudad de Granada. Concretamente, el conocimiento sobre barreras de acceso que las mujeres y los hombres inmigrantes pueden tener para hacer uso de un servicio público como es la formación profesional. El estudio presenta el material resultante de un trabajo de investigación en el marco de la especialización del autor en sociología de la educación. Aparte del material descriptivo sobre la nueva realidad de la formación profesional en España y Andalucía, se han utilizado técnicas cualitativas basadas en entrevistas en profundidad a «entrevistados clave» de la comunidad educativa, además, también hemos entrevistado a actores institucionales y cuasi institucionales. El análisis se ha organizado a partir de tres bloques básicos: la filosofía subyacente en la nueva realidad de la formación profesional reglada en España, la aplicación de un modelo de interacción entre los diferentes actores de la comunidad educativa y, por último, se pretende comprobar que no está motivada la idea existente de rechazo a las personas inmigrantes cuando acceden a los cursos de formación profesionalThis article outlines the results of an analysis of formal vocational training in a local context, the city of Granada. Concretely, offers knowledge about access barriers that immigrant women and men face when using a public service such as formal vocational training. This study presents the resultant research within the framework of sociology of education, the area of specialization of the author. In addition to describing the new reality of formal vocational training in Spain and Andalusia, this article employs qualitative technologies based on in-depth interviews with key members of the Educational Community as well as institutional and quasi-institutional actors. The analysis has been organised in three basic parts. First, we analyse the philosophy underlying the new reality of formal vocational training in Spain. Next, we apply an interaction model between the different actors of the Educational Community. Finally, we attempt to verify that there are no reasons for endorsing the existing idea that immigrant persons are rejected when they access vocational training courses

On Rules and Parameter Free Systems in Bounded Arithmetic

We present model–theoretic techniques to obtain conservation results for first order bounded arithmetic theories, based on a hierarchical version of the well known notion of an existentially closed model.Ministerio de Educación y Ciencia MTM2005-0865

Existentially Closed Models and Conservation Results in Bounded Arithmetic

We develop model-theoretic techniques to obtain conservation results for first order Bounded Arithmetic theories, based on a hierarchical version of the well-known notion of an existentially closed model. We focus on the classical Buss' theories Si2 and Ti2 and prove that they are ∀Σbi conservative over their inference rule counterparts, and ∃∀Σbi conservative over their parameter-free versions. A similar analysis of the Σbi-replacement scheme is also developed. The proof method is essentially the same for all the schemes we deal with and shows that these conservation results between schemes and inference rules do not depend on the specific combinatorial or arithmetical content of those schemes. We show that similar conservation results can be derived, in a very general setting, for every scheme enjoying some syntactical (or logical) properties common to both the induction and replacement schemes. Hence, previous conservation results for induction and replacement can be also obtained as corollaries of these more general results.Ministerio de Educación y Ciencia MTM2005-08658Junta de Andalucía TIC-13

Fragments of Arithmetic and true sentences

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the ¦n+1–sentences true in the standard model is the only (up to deductive equivalence) consistent ¦n+1–theory which extends the scheme of induction for parameter free ¦n+1–formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first–order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain results on the quantifier complexity, (non)finite axiomatizability and relative strength of schemes for ¢n+1–formulas.Junta de Andalucía TIC-13

Envelopes, indicators and conservativeness

A well known theorem proved (independently) by J. Paris and H. Friedman states that BΣn +1 (the fragment of Arithmetic given by the collection scheme restricted to Σn +1‐formulas) is a Πn +2‐conservative extension of IΣn (the fragment given by the induction scheme restricted to Σn ‐formulas). In this paper, as a continuation of our previous work on collection schemes for Δn +1(T )‐formulas (see [4]), we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2‐conservative extension of T . We prove that this conservativeness property is equivalent to a model‐theoretic property relating Πn ‐envelopes and Πn ‐indicators for T . The analysis of Σn +1‐collection we develop here is also applied to Σn +1‐induction using Parsons' conservativeness theorem instead of Friedman‐Paris' theorem. As a corollary, our work provides new model‐theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos (see [8]): BΣn +1 and IΣn +1 are Σn +3‐conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1.Junta de Andalucía TIC-13

On the quantifier complexity of Δ n+1 (T)– induction

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]).Ministerio de Educación y Cultura DGES PB96-134