We give an elementary theory of Henselian local rings and construct the Henselisation of a local ring. All our theorems have an algorithmic content.

We give a definition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a (...) uniform definition by an existential formula and neither by a universal formula for the valuation rings of all the finite extensions of a given Henselian valued field. We also show that there is no existential formula of the ring language defining Zp inside Qp uniformly for all p. For any fixed finite extension of Qp, we give an existential formula and a universal formula in the ring language which define the valuation ring. (shrink)

This article is a logical continuation of the Henri Lombardi and Franz-Viktor Kuhlmann article [9]. We address some classical points of the theory of valued fields with an elementary and constructive point of view. We deal with Krull valuations, and not simply discrete valuations. First of all, we show how to construct the Henselization of a valued field; we restrict to fields in which one has at one's disposal algorithmic tools to test the nullity or the valuation ring membership. It (...) is therefore a work that differs as much in spirit as in field of application from that of Mines, Richman and Bridges , who address the framework of Heyting fields and discrete valuation. We show then in a constructive way a batch of classical results in Henselian fields, notably factorization criteria and Krasner's Lemma. We conclude by a construction of the inertia field of a valued field. (shrink)

We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued field is stably embedded in an elementary extension if and only if its value group is stably embedded in its corresponding extension, its residue field is stably embedded in its corresponding extension, and the extension of valued fields satisfies a certain algebraic condition. We show for instance that all types over the (...) Hahn field $$\mathbb {R}((\mathbb {Z}))$$ are definable. Similarly, all types over the quotient field of the Witt ring $$W(\mathbb {F}_p^{\text {alg}})$$ are definable. This extends a work of Cubides and Delon and of Cubides and Ye. (shrink)

Given a Henselian valuation, we study its definability (with and without parameters) by examining conditions on the value group. We show that any Henselian valuation whose value group is not closed in its divisible hull is definable in the language of rings, using one parameter. Thereby we strengthen known definability results. Moreover, we show that in this case, one parameter is optimal in the sense that one cannot obtain definability without parameters. To this end, we present a (...) construction method for a t-Henselian non-Henselian ordered field elementarily equivalent to a Henselian field with a specified value group. (shrink)

In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely Henselian valued fields of equicharacteristic $0$, algebraically closed valued fields, algebraically maximal Kaplansky valued fields, and unramified mixed characteristic Henselian valued fields with perfect residue field. First, we compute the burden of such a valued field in terms of the burden of its value group and its residue field. The burden is a cardinal related to the model theoretic complexity and a (...) notion of dimension associated to $\text {NTP}_2$ theories. We show, for instance, that the Hahn field $\mathbb {F}_p^{\text {alg}})$ is inp-minimal, and that the ring of Witt vectors $W$ over $\mathbb {F}_p^{\text {alg}}$ is not strong. This result extends previous work by Chernikov and Simon and realizes an important step toward the classification of Henselian valued fields of finite burden. Second, we show a transfer principle for the property that all types realized in a given elementary extension are definable. It can be written as follows: a valued field as above is stably embedded in an elementary extension if and only if its value group is stably embedded in the corresponding extension of value groups, its residue field is stably embedded in the corresponding extension of residue fields, and the extension of valued fields satisfies a certain algebraic condition. We show, for instance, that all types over the power series field $\mathbb {R})$ are definable. Similarly, all types over the quotient field of $W$ are definable. This extends previous work of Cubides and Delon and of Cubides and Ye.These distinct results use a common approach, which has been developed recently. It consists of establishing first a reduction to an intermediate structure called the leading term structure, or $\operatorname {\mathrm {RV}}$ -sort, and then of reducing to the value group and residue field. This leads us to develop similar reduction principles in the context of pure short exact sequences of abelian groups.prepared by Pierre Touchard.E-mail: [email protected]: https://miami.uni-muenster.de/Record/a612cf73-0a2f-42c4-b1e4-7d28934138a9. (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)

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)

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 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)