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.

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)

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.

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)

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)

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)

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)

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.

Combining textual, visual, and ethnographic approaches to discourse, this article examines a variety of resources employed in the narrative construction of Washington, DC’s Chinatown in a billboard advertisement that de-ethnicizes the neighborhood. Analysis of the linguistic resources of narrative structure, comparative reference, and lexical cohesion reveals how the gentrification of Chinatown is constructed as a positive transformation driven by a corporation. Further, the visual juxtaposition of text with photos and graphics appropriates the community voice and infuses it with corporate identity. (...) This ideological multimodal construction of the transformation of Chinatown is finally actualized in its durable material form and strategic spatial emplacement. Incorporating ethnographic observation and an interview, this article illustrates how the symbolic power of narrative in place-making is interdependent on the economic power of its producer to propagate ideological discourse in the material world. (shrink)

This article takes Heidegger's design distinctions for human being [Dasein] including affectivity, understanding, and speech, and, using these distinctions, generates a Heideggerian definition of empathy [Einfuehlung]. This article distinguishes empathic receptivity, empathic understanding, empathic interpretation, and empathic speech (or responsiveness). It also looks at characteristic breakdowns.

The distinction between “empathy” and “sympathy” in the context of ethics is a dynamic and challenging one. The eighteenth century texts of David Hume and Adam Smith used the word "sympathy," but not "empathy," although the conceptual distinction marked by empathy was doing essential work in their writings. After discussing the early uses of these terms, this article is organized historically. Two traditions are distinguished. The first is the Anglo-American tradition, and it extends from Hume and Smith to the twenty-first (...) century work of Michael Slote. Stephen Darwall’s contribution is applied in engaging Hume and Smith. Finally, the interrelation of empathy, sympathy and altruism is explored in the work of John Rawls and Thomas Nagel. The second tradition is the Continental one. It extends from the spirituality of Johann Herder to the phenomenological movement of Edmund Husserl, Martin Heidegger, Max Scheler, and Edith Stein. The intentional analysis of empathy is directly relevant to the constitution of the social community in a broad, normative relationship with the "Other.". (shrink)

Heidegger famously said that the best treatment of the emotions in western history was Book 2 of Aristotle's RHETORIC. Heidegger then did an analysis of this material prior to the publication of Being and TIme (1927). This engages engages with Heidegger's treatment of Aristotle's treatment of the emotions in relation to Heidegger's design distinction of affectivity (Befindlichkeit), understanding, and discourse (Rede).

We defend in this essay Paul Ricœur’s hermeneutics of suspicion against Toril Moi’s debunking of it as a misguided interpretation of the practice of critical inquiry, and we relate the practice of a rigorous and critical empathy to the hermeneutics of suspicion. For Ricœur, empathy would not be a mere psychological mechanism by which one subject transiently identifies with another, but the ontological presence of the self with the Other as a way of being —listening as a human action that (...) is a fundamental way of being with the Other in which “hermeneutics can stand on the authority of the resources of past ontologies.” In a rational reconstruction of what a Ricœur-friendly approach to empathy would entail, a logical space can be made for empathy to avoid the epistemological paradoxes of Husserl and the ethical enthusiasms of Levinas. How this reconstruction of empathy would apply to empathic understanding, empathic responsiveness, empathic interpretation, and empathic receptivity is elaborated from a Ricœurian perspective. (shrink)

Technology acceptance by users has been extensively studied in recent years in various fields such as technologies for learning, e-commerce, and business technologies. This review focuses specifically on Human Resource Information Systems and its acceptance by users. Given their widespread use in organisations, HRIS acceptance has been researched but not synthesised in any way. This article aims to review the effectiveness of the classical TAM and UTAUT models commonly used for new technologies and to identify the variables added to these (...) models to better predict HRIS acceptance by employees. It also highlights the importance of the human-machine-organisation relationship to contribute to the understanding of HRIS acceptance in professional environments. This review confirms the effectiveness of the TAM and UTAUT models and proposes to develop them by variables reffering to technological characteristics, user satisfaction with the system, and organisational variables. The discussion focuses on the retroaction possibilities between the different Human-Machine-Organisation relation levels. (shrink)

This article theorises the process of adapting my research on intercultural communication for public performance in collaboration with a theatre company. I frame the collaboration as taking place within a hospitable institutional space, and then consider what it means to enact hospitality interpersonally, given Derrida's understanding that the condition of its possibility is at the same time the condition of its impossibility. I suggest that the enactment of hospitality can be understood through the application of an intercultural theoretical framework based (...) on Mikhail Bakhtin's concept of outsideness, and that this framework can be applied to both the collaboration with the theatre company and to the purposes of public engagement with research. I conclude with a consideration of the relationship between hospitality and hope, and a call to move towards a ‘condition of possibility’ for working as academics, for public engagement, and for living. (shrink)

This paper explores violence in intimate relationships in one low-income community in the Western Cape, South Africa. In this community most intimate relationships (including parentchild, intimate partner relationships and friendships) seem to be characterized by anger, rage and also violence. In our analysis we discuss how the concepts of shame, guilt and the compulsion to repeat can serve to illuminate the seemingly inevitable link between violence and care in this specific community. It also seems that contextual factors such as class, (...) gender and race shape not only the form violence assumes, but also to whom it is directed. While we pay attention to the material and ideological conditions that shape the lives of individual storytellers, we also focus on the ways in which violence is represented in the individual stories. (shrink)

In recent years, increasing attention has been paid to the all-around development and mental health of students in education. Positive education, a rapidly developing ramification of positive psychology, has proved beneficial to students’ learning and wellbeing. Meanwhile, online learning has quickly gained popularity due to the impact of COVID-19. However, there have been few reports discussing the relationship between positive education and online learning by combining theories and practices. To explore the connection between positive education and online learning, we provide (...) a literature review for studies, mostly between 2010 and 2022, of theories and practices for both positive education and online learning. Next, we establish one-to-one links between the relevant theories and practices of online learning to each domain in the PERMA model of positive education, a theoretical framework including Positive emotion(P), Engagement(E), Relationship(R), Meaning(M), and Accomplishment(A). We aim to explore how to promote the development of positive education by applying the theoretical and practical advantages of online learning to the PERMA framework of positive education. This study aims to enrich the research perspectives of positive education and provide a reference for future research. (shrink)

This work presents a conception of Hume's overall philosophical stance which is derived from a focus on his Dialogues Concerning Natural Religion and The Natural History of Religion. A broad context is provided by frequent references to A Treatise of Human Nature and to An Enquiry Concerning Human Understanding as well as to other relevant essays and letters written by Hume. Religious Naturalism is a complex tapestry woven of aesthetic, ethical, epistemological and metaphysical elements. The religious element in Hume's writings, (...) which some commentators see as a transcendent position, is interpreted as an immanentist religiosity akin to that of Spinoza and Einstein. Hume's three "strong natural beliefs" in "self", objects and causality, come together as a metaphysical faith in the ultimate reality of a shared cosmos. Hume's aesthetic response is expressed as a sense of the sublimity of the cosmos even in the midst of skeptical doubt. In Hume's religious naturalism his epistemological skepticism casts doubt on and tempers his metaphysical faith. It is shown that Hume's overriding ethical concern was to further the happiness of humanity by replacing the "pernicious superstition" of supernaturalism with an immanentist position which affirms the inexplicable presence of an eternal cosmos. This position is what is here termed Religious Naturalism. (shrink)

On the face of it, normative conflicts are commonplace. Yet standard deontic logic declares them to be logically impossible. That prompts the question, What are the proper principles of normative reasoning if such conflicts are possible? This paper examines several alternatives that have been proposed for a logic of 'ought' that can accommodate normative conflicts, and finds all of them unsatisfactory as measured against three criteria of adequacy. It then introduces a new logic that does meet all three criteria, and (...) so allows for the possibility of genuine normative conflicts. (shrink)