Let T be a complete o-minimal extension of the theory of real closed fields. We characterize the convex hulls of elementary substructures of models of T and show that the residue field of such a convex hull has a natural expansion to a model of T. We give a quantifier elimination relative to T for the theory of pairs (R, V) where $\mathscr{R} \models T$ and V ≠ R is the convex hull of an elementary substructure of R. We deduce (...) that the theory of such pairs is complete and weakly o-minimal. We also give a quantifier elimination relative to T for the theory of pairs (R, N) with R a model of T and N a proper elementary substructure that is Dedekind complete in R. We deduce that the theory of such "tame" pairs is complete. (shrink)

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables the result takes (...) a still simpler form, and we derive in this way the polynomial-time decidability of the sets defined by such formulas. (shrink)

We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define (...) composition of LE-series and establish its basic properties, including the existence of compositional inverses. Various interesting subfields of the field of LE-series are also considered. (shrink)

I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...) value group Γ. In [9] we expanded the ordered fieldto a model ofTas follows. Take a tame elementary substructure′ ofsuch thatR′ ⊆VandR′maps bijectively ontounder the residue class map, and make this bijection into an isomorphism′ ≌ofT-models. (We showed such′ exists, and that this gives an expansion ofto aT-model that is independent of the choice of′.). (shrink)

Related Works: Original Paper: Lou Van Den Dries. $T$-Convexity and Tame Extensions II. J. Symbolic Logic, Volume 62, Issue 1 , 14--34. Project Euclid: euclid.jsl/1183745182.

For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

Vector spaces over fields are pseudofinite, and this remains true for vector spaces over division rings that are finite-dimensional over their center. We also construct a division ring such that the nontrivial vector spaces over it are not pseudofinite, using Richard Thompson's group F. The idea behind the construction comes from a first-order axiomatization of the class of division rings all whose nontrivial vector spaces are pseudofinite.

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.

In lieu of an abstract, here is a brief excerpt of the content:BreathingLuk Van den Dries (bio)This text, "Breathing," was conceived for the book From Act to Acting: Fabre's Guidelines for the Performer of the 21st Century (2021). The book was conceived and designed by Jan Fabre, author, theatre artist, and visual artist, active since the 1970s. The book was written by Luk Van den Dries, dramaturg and theatre researcher of the University of Antwerp, in tight collaboration with (...) Jan Fabre and the three most important performers/teachers of the Belgian theatre company, Troubleyn (Annabelle Chambon, Cédric Charron, and Ivana Jozic). The book sheds new light on the physical, mental, and vocal training of the performer and furthermore gives insight into Fabre's revolutionary thoughts on contemporary theatre.1Breathing is the first of the ten performative principles that together create the basic grammar in which the language of the performers is grounded.Three-phased breathing (one part in, one part out, one part nothing) is a basic condition in the series of exercises Jan Fabre developed throughout his career. This respiration technique returns in all exercises. Also, it is the first principle that the performers are taught: by dividing breathing into three equal parts, energy is built up and stress or fatigue is canalized. It is a way to rebalance, to find a place of rest after a strenuous effort, or it can also be used as a springboard to a heightened performance. Very regularly during individual exercises, Fabre will refer to this respiration technique, especially in specific situations of high adrenaline, but of course the performers should learn to use this respiration technique autonomously. They should become so familiar with the rhythm of this breathing that they automatically fall back on it when necessary. Because this respiration technique is so crucial to Fabre's acting pedagogy, it is described in detail as the very first exercise in his book. Its basic principles are explained below as well, as the first performative principle.Breathing is a sign of life, and on this primal and essential level it needs to be understood that, through breathing, the performer gives life. He breathes life into the performance. Fabre himself has described this basic condition for the birth of theatre through breathing very precisely: [End Page 30]The most important weapon of the warrior of beauty is his respiration. When the performance starts, life stops. Life itself dies. The warrior of beauty is alive, but life itself is dead. The warrior of beauty remains with just his own breath. When he enters the stage, he needs to breathe life into deceased life. Like a god gives his breath to create life. In the same way he will create life with his breath. How will he achieve this? By breathing correctly: one-third inhaling through the nostrils, one-third exhaling through pursed lips, one-third without breathing. And then the miracle happens. The breath becomes imagination and the imagination breathes. The warrior of beauty is the master of breath and life.2Fabre's abdominal breathing differs from regular forms of breathing, such as techniques derived from Asian yoga techniques, Chi-kung or Tai-chi, as it stresses different parts. At the same time, it is closely related to it, because these practices also adopt the notion that breathing in the first place rouses vitality and spirit and that the right kind of breathing thus aims at controlling life currents and bringing about a clear mind. In yoga it is called pranayama: prana meaning spirit or force of life, ayama meaning 'control' or 'grasp.' Yoga knows many variants in directing the breath, depending on the asanas (yoga postures) in which they are bedded. Sometimes focusing mainly on the diaphragm and the flanks, sometimes on abdominal breathing. Also, suspending your breath (kumbhaka) is a yoga technique, applied at the end of inhalation as well as after exhalation and during taking breath.In Fabre's case, abdominal breathing is stressed: first, air is inhaled through the nose, subsequently sent in the direction of the peritoneal cavity and the flanks, and then again exhaled via a very precise blowing technique (a dosed flow of air through an imaginary straw). During the cycle the diaphragm remains... (shrink)

We use a new construction of an o-minimal structure, due to Lipshitz and Robinson, to answer a question of van den Dries regarding the relationship between arbitrary o-minimal expansions of real closed fields and structures over the real numbers. We write a first order sentence which is true in the Lipshitz-Robinson structure but fails in any possible interpretation over the field of real numbers.

§1. Introduction. Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the ‘large-scale structure’ of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the completeness of the metric space, now follow rather easily from saturation properties of ultrapowers, and in this survey, we want to present two applications of the van den Dries-Wilkie approach. (...) Using ultrapowers we obtain an explicit description of the asymptotic cone of a semisimple Lie group. From this description, using semi-algebraic groups and non-standard methods, we can give a short proof of the Margulis Conjecture. In a second application, we use set theory to answer a question of Gromov.§2. Definitions. The intuitive idea behind Gromov's concept of an asymptotic cone was to look at a given metric space from an ‘infinite distance’, so that large-scale patterns should become visible. In his original definition this was done by gradually scaling down the metric by factors 1/nfornϵ ℕ. In the approach by van den Dries and Wilkie, this idea was captured by ultrapowers. Their construction is more general in the sense that the asymptotic cone exists for any metric space, whereas in Gromov's original definition, the asymptotic cone existed only for a rather restricted class of spaces. (shrink)

Este artículo sostiene que Platón constituye un interlocutor fructífero para la Teoría crítica. Desde un diálogo con Axel Honneth, argumentaremos primero que la metodología de crítica social desarrollada en la República posee elementos constructivo-racionales y reconstructivo-hermenéuticos. Luego, enfatizaremos dos conceptos prefigurados en dicha obra que, mediante Hegel, yacen en el trasfondo de la Teoría crítica, a saber: holismo y patología social. Ello nos permitirá articular, como conclusión, una “dialéctica de la justicia” que, en el sentido de Adorno & Horkheimer, recorre (...) la obra de Honneth. (shrink)

A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of Lascar U-rank a power of ω and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding an integral domain, while not pregeometric in general, do have a unique existential matroid. Generalising previous results by van den Dries, we define dense elementary pairs of structures expanding (...) an integral domain and with an existential matroid, and we show that the corresponding theories have natural completions, whose models also have a unique existential matroid. We also extend the above result to dense tuples of structures. (shrink)

L. van den Dries proved that the theory of n-valued rings has a model companion. We show here that this result is still true when the valuation rings are required to satisfy given inclusion relations (we restrict ourselves to the case of residual characteristic zero).

BackgroundWith advances in sequencing technologies, increasing numbers of people are being informed about a genetic disease identified in their family. In current practice, probands are asked to inform at-risk relatives about the diagnosis. However, previous research has shown that relatives are sometimes not informed due to barriers such as family conflicts. Research on family communication in genetic diseases aims to explore the difficulties encountered in informing relatives and to identify ways to support probands in this.Main bodyResearch on family communication may (...) also reveal that participants did not inform their relatives about the risk of a serious genetic condition, even when preventive and treatment options are available. Researchers may then face a dilemma: Do they need to warn at-risk relatives about the finding? Or do they keep silent due to prior confidentiality agreements with study participants?ConclusionsWe believe that the absolute confidence promised to research participants outweighs the interests of their relatives, even though it can be claimed that relatives at risk of a genetic disease do, in principle, have a right to know information collected about their health. Not respecting confidentiality agreements could cause distrust between researchers and research participants and possibly harm the relationship between probands and relatives. Relatives' health interests can still be taken into account without jeopardizing participant trust, by considering alternative scenarios, including sharing general study findings on the barriers participants experience with their healthcare professionals and by offering participants psychosocial support for family communication. (shrink)

Libertarian paternalism involves the idea that it is justified to shape the context in which people make important choices in a way that they are nudged to options that would be better for them, wh...

ABSTRACTBoth auditory and visual emotional memories can be made less emotional by loading working memory during memory recall. Taxing WM during recall can be modality specific (giving an audit...

Several authors have pointed at opportunities to develop the well-established Business Balanced Scorecard into a Scorecard that enables companies to integrate sustainability into their strategy. Recent case studies and research experiences show that social and environmental targets are more widely recognized as strategic drivers for management. However, experiments also show that the traditional Scorecard has its limits when it comes to e.g. stakeholder management and product chain management. The European Corporate Sustainability Framework(ECSF) program distinguishes several ambition levels for Corporate Sustainability/corporate (...) Responsibility. The traditional Balanced Scorecard is suitable for companies that aim for Compliance-driven CS/cror for Profit-driven CS/cr, where the financial bottom line is the ultimate indicator for success. More ambitious companies want to balance economic, social and ecological targets in a Community-driven CS/sror Synergy-driven CS/cr.For ambitious companies, we propose a format of a Responsive Business Scorecard (RBS). The Responsive Scorecard enables companies to score at Profit, People and Planet, at the same time to integrate stakeholder demands into internal programs to improve performance. The RBS includes five Perspectives: Customers&Suppliers, Financiers&Owners, Society&Planet, Internal Process and Employees&Learning.We assessed the practical feasibility of a Responsive Scorecardin food and tourist industries. In the food industry, we analyzed whether existing business priorities of Italian companies can adequately fill a Responsive scorecard.Our conclusion is that traditional topics like finance, customers and employees are readily filled, but that sustainability topics like chain management (suppliers) and environmental performance (planet) need further elaboration. The tourist sector is dominated by Small and Medium Sized Enterprises. We investigated whether existing eco-labels for camping-sites and marinas can be developed into Responsive Scorecards. Our conclusion is that such a sector specific development of a Responsive Scorecard is possible. Further research has to show what is the value added of the new scorecard for companies in the tourist sector. (shrink)

This book offers a comprehensive overview of current developments in the field of Responsible Research and Innovation (RRI). Divided into three parts, the book first presents reflections on the concept of RI from various angles: how did it come about, who is involved and how might in be applied in various contexts, such as the academic environment or in developing countries. The second part discusses the actual application of RRI to technology development: for climate engineering, water management and energy technology (...) along with a general discussion on how to integrate RRI in innovation trajectories. The last part offers a closer look at the application of RRI to the business context. This part offers lessons from comparable concepts such as social and sustainability innovation as well as insights from two case-studies, one in the food sector and the other in data management. As a whole, the book contributes to the ongoing development of the framework of RRI by giving an overview of the state-of-the art research, presenting the lessons learned from several case studies, and showing the way for future application of RI in other fields and cultural contexts, such as industry and developing countries. (shrink)

Ethical issues of information and communication technologies (ICTs) are important because they can have significant effects on human liberty, happiness, and people’s ability to lead a good life. They are also of functional interest because they can determine whether technologies are used and whether their positive potential can unfold. For these reasons, policy makers are interested in finding out what these issues are and how they can be addressed. The best way of creating ICT policy that is sensitive to ethical (...) issues pertain to being proactive in addressing such issues at an early stage of the technology life cycle. The present paper uses this position as a starting point and discusses how knowledge of ethical aspects of emerging ICTs can be gained. It develops a methodology that goes beyond established futures methodologies to cater for the difficult nature of ethical issues. The authors outline how the description of emerging ICTs can be used for an ethical analysis. (shrink)