Local induction and provably total computable functions

Let I¦− 2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free ¦2 formulas. Answering a question of R. Kaye, L. Beklemishev showed that the provably total computable functions of I¦− 2 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 I¦− 2 . In this way, we obtain a more direct answer to Kaye’s question, avoiding the metamathematical machinery (reflection principles, provability logic,...) needed for Beklemishev’s original proof. Our methods are model–theoretic and allow for a general study of I¦− n+1 for all n ¸ 0. In particular, we derive a new conservation result for these theories, namely that I¦− n+1 is ¦n+2–conservative over I§n for each n ¸ 1.Ministerio de Ciencia e Innovación MTM2008–06435Ministerio de Ciencia e Innovación MTM2011–2684

Local Induction and Provably Total Computable Functions: A Case Study

Let IΠ−2 denote the fragment of Peano Arithmetic obtained by restricting the induction scheme to parameter free Π2 formulas. Answering a question of R. Kaye, L. Beklemishev showed that the provably total computable functions (p.t.c.f.) of IΠ−2 are, precisely, the primitive recursive ones. In this work we give a new proof of this fact through an analysis of the p.t.c.f. of certain local versions of induction principles closely related to IΠ−2 . This analysis is essentially based on the equivalence between local induction rules and restricted forms of iteration. In this way, we obtain a more direct answer to Kaye’s question, avoiding the metamathematical machinery (reflection principles, provability logic,...) needed for Beklemishev’s original proof.Ministerio de Ciencia e Innovación MTM2008–0643

Rethinking Ephemeral Architecture. Advanced Geometry for Citizen-Managed Spaces

In recent years there have been a high amount of citizen initiatives that address the complex problems of the contemporary city. There are empty or disused spaces that have been reused for urban gardens, for social use, to encourage integration and civic activities activation, etc. Traditional architectural processes do not provide realistic solutions to these initiatives that, along with limited financial resources, have led to the emergence of architectures and self-constructed facilities, almost as an emergency mode, without necessary planning, media and constructive knowledge. The democratization of technology, thanks to laboratories of digital production, combined with knowledge of the properties of different surfaces through the CAD-CAM tools, offers new opportunities for the development of a lightweight, flexible and low impact architecture, very according to the needs of citizens' initiatives that naturally arise in our cities. The new existing scenario contemplates the figure of the architect, or engineer, not only as an agent of the market, but as a professional able to propose efficient solutions to problems from within, bringing their specific knowledge and serving as bridges between the new technological solutions and the challenges of society

Existentially Closed Models in the Framework of Arithmetic

We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.Ministerio de Educación y Ciencia MTM2011–2684

Note: Tormenta: An open source Python-powered control software for camera based optical microscopy

Until recently, PC control and synchronization of scientific instruments was only possible through closed-source expensive frameworks like National Instruments' LabVIEW. Nowadays, efficient cost-free alternatives are available in the context of a continuously growing community of open-source software developers. Here, we report on Tormenta, a modular open-source software for the control of camera-based optical microscopes. Tormenta is built on Python, works on multiple operating systems, and includes some key features for fluorescence nanoscopy based on single molecule localization.Fil: Barabas, Federico Martín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias ; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Masullo, Luciano Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias ; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Stefani, Fernando Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias ; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentin

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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