We prove the triviality of the Grothendieck ring of a Z-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K 2 to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

We prove the triviality of the Grothendieck ring of a $\mathbb{Z}$-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K$^2$ to itself minus a point. When we specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex (...) numbers contains as a subring the ring of integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings. (shrink)

We recall the notions of weak and strong Euler characteristics on a first order structure and make explicit the notion of a Grothendieck ring of a structure. We define partially ordered Euler characteristic and Grothendieck ring and give a characterization of structures that have non-trivial partially ordered Grothendieck ring. We give a generalization of counting functions to locally finite structures, and use the construction to show that the Grothendieck ring of the complex (...) numbers contains as a subring the ring of integer polynomials in continuum many variables. We prove the existence of a universal strong Euler characteristic on a structure. We investigate the dependence of the Grothendieck ring on the theory of the structure and give a few counter-examples. Finally, we relate some open problems and independence results in bounded arithmetic to properties of particular Grothendieck rings. (shrink)

We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic (...) geometry a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

Introduction -- Otherness in contemporary European cinema -- Potential and limits of a new European in Nicolas Echevarría's Cabeza de vaca -- Migrants in Europe: breaking the boundaries? -- Inspiration from abroad? cultural boundaries in Chicano cinema -- Conclusion.

Study on Budhist Pramāṇa-vāda (doctrine of proof: an epistemological study of the nature of knowledge) and Hetu-vidya (science of causes: a system of logic).

"Der vorliegende Band vereinigt die Beitrèage des Symposiums zur Logik der Stoiker und ihrer Vorlèaufer, das vom 1.-7.9.1991 in Bamberg stattfand"--P. [7].

Interfirm collaboration and trust are topics currently exciting research interest. The literature treats trust as a unitary concept, providing little understanding of those processes that create trust, or are employed by parties relying on trust. I suggest that two distinct forms of trust can be observed in economic exchanges: fragile trust and resilient trust. I define these kinds of trust, speculate on processes by which economic actors learn about them, and explore contexts in which they are likely to be relied (...) upon by economic actors. I conclude with a discussion of implications for practice and scholarship. (shrink)

ABSTRACT Sexting has become a prominent part of adolescent culture. Under current laws, adolescents caught sexting are being arrested, facing child pornography charges, and having to register as sex offenders. State laws on child pornography and child abuse differ throughout the United States and conflict with federal laws, making the ethical obligations for psychologists unclear. The purpose of this article is to promote awareness about legal obligations regarding adolescent sexting, address the ethical dilemma that psychologists face when adolescent sexting is (...) disclosed during psychological treatment, and to provide implications and recommendations for psychologists. (shrink)

This paper provides evidence for the following novel insights: (1) People’s economic decisions depend on their psychological motives, which are shaped predictably by the social context. (2) In particular, the social context influences people’s other-regarding preferences, their beliefs and their perceptions. (3) The influence of the social context on psychological motives can be measured experimentally by priming two antagonistic motives—care and anger—in one player towards another by means of an observance or a violation of a fairness norm. Using a mediation (...) approach, we find that the care motive leads to higher levels of cooperation which are driven by more optimistic beliefs, a different perception of the game as well as by a shift towards more pro-social preferences. (shrink)

This paper explores how the virtuous aesthetic cosmopolitan—one actively engaged in cultivating an authoritative appreciation for culturally unfamiliar works or traditions of art, in a manner informed by moral cosmopolitan principles—engages with the ‘exotic’ artwork in a manner that is both morally responsible and aesthetically discerning. After providing an overview of philosophical cosmopolitanism and the aesthetic cosmopolitan’s project, I consider in depth a particular example: the music of Mauritanian singer Noura Mint Seymali as encountered by an unaccustomed listener. I explore (...) potential problematic responses to the work, including both chauvinistic and exoticizing responses. I then consider possible strategies for alternative responses, informed by the aesthetic and hermeneutic theories of Hume, Gadamer, and Charles Taylor. Having revealed deficiencies with these alternatives, I go on to argue that the cosmopolitan’s best strategy is a mode of appreciation that is ‘conversational’ in nature, an open-ended approach modeled on an exchange between the appreciator and an other-cultural interlocutor. In proposing such a model, I draw on the work of Kwame Appiah and Maria Lugones, as well as Anthony Laden’s recent work on conversational norms. (shrink)

Study on Pratītyasamutpāda, theory of relativity and causality in Buddhism with reference to canonical literature.

v. 1. General moral theology -- v. 2. The truth will set you free.

Community acts of material signification are an important form of sculpture that occur through an exchange of human and non-human agents. First these acts of sculpture are discussed in relation to extended mind, the morphogenic model of making, material engagement theory and entanglement to frame how humans shape the world as collaborators with non-humans by extending mind through material. I then discuss various acts of community material accumulation that I consider sculpture, skateboarding and clay forming as evidence of extended mind, (...) comparison of the morphogenic to the hylomorphic model of making, occurrences of materials affecting other materials absent of human intervention and my recent participatory installation Stone Fruit. These topics are used to present a lens for understanding the production of sculpture as a collaboration with opposed to dictation on systems of materials, places and people. This lens, in turn, presents community sites of material accumulation to be an important form of sculpture production. (shrink)