The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is (...) model complete and the theory Art l is companionable, with model-companion Got l. (shrink)

In this work we introduce a class of commutative rings whose defining condition is that its lattice of ideals, augmented with the ideal product, the semi-ring of ideals, is isomorphic to an MV-algebra. This class of rings coincides with the class of commutative rings which are direct sums of local Artinian chain rings with unit.

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by ’t Hooft. We view these ontological states as the ones embedded with realism and compare them to the quantum states that represent superpositions, viewing the latter as mere information of the system they describe. Such a deterministic model puts forward conditions for the applicability of Bell’s inequality: the usual (...) inequality cannot be applied to the usual experiments. We build a Bell-like inequality that can be applied to the EPR scenario and show that this inequality is always satisfied by QM. In this way we show that QM can indeed have a local interpretation, and thus meet with the causal structure imposed by the Theory of Special Relativity in a satisfying way. (shrink)

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 present numerous natural algebraic examples without the so-called Canonical Base Property (CBP). We prove that every commutative unitary ring of finite Morley rank without finite-index proper ideals satisfies the CBP if and only if it is a field, a ring of positive characteristic or a finite direct product of these. In addition, we construct a CM-trivial commutative local ring with a finite residue field without the CBP. Furthermore, we also show that finite-dimensional non-associative algebras over an algebraically closed (...) field of characteristic [Formula: see text] give rise to triangular rings without the CBP. This also applies to Baudisch’s [Formula: see text]-step nilpotent Lie algebras, which yields the existence of a [Formula: see text]-step nilpotent group of finite Morley rank whose theory, in the pure language of groups, is CM-trivial and does not satisfy the CBP. (shrink)

In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls (...) prey to radical local indeterminism, the Leibniz algebras do not. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. Moreover, the motivation for the program--that isomorphic substantival models should be regarded as representing the same physical situation--is misguided. (shrink)

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 show that if M is a strongly minimal large homogeneous structure in a countable similarity type and the pregeometry of M is locally modular but not modular, then the pregeometry is affine over a division ring.

Familial determination, replete with its frequent usurping of patient autonomy, propagation of collusion, and circumnavigation of direct patient involvement in their own care deliberations, continues to impact clinical practice in many Asian nations. Suggestions that underpinning this practice, in Confucian-inspired societies, is the adherence of the populace to the familial centric ideas of personhood espoused by Confucian ethics, provide a novel means of understanding and improving patient-centred care at the end of life. Clinical experience in Confucian-inspired Singapore, however, suggests that (...) personhood is conceived in broader terms. This diverging view inspired a study of local conceptions of personhood and scrutiny of the influence of the family upon it. From the data gathered, a culturally appropriate, clinically relevant and ethically sensitive concept of personhood was proposed: the Ring Theory of Personhood that better captures the nuances of local conceptions of personhood. The Ring Theory highlights the fact that, far from being solely dependent upon familial centric ideals, local conceptions of personhood are dynamic, context dependent, evolving ideas delineated by four dimensions. Using the Ring Theory, the nature of familial influences upon the four dimensions of personhood – the Innate, Individual, Relational and Societal – are examined to reveal that, contrary to perceived knowledge, conceptions of personhood within Confucian societies are not the prime reason for the continued presence of this decision-making model but remain present within local thinking and practices as a sociocultural residue and primarily because of inertia in updating ideas. (shrink)

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit (...) during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement. (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)

Directional deep brain stimulation contacts provide greater spatial flexibility for therapy than traditional ring-shaped electrodes, but little is known about longitudinal changes of impedance and orientation. We measured monopolar and bipolar impedance of DBS contacts in 31 patients who underwent unilateral subthalamic nucleus deep brain stimulation as part of a randomized study. At different follow-up visits, patients were assigned new stimulation configurations and impedance was measured. Additionally, we measured the orientation of the directional lead during surgery, immediately after surgery, and (...) 1 year later. Here we contrast impedances in directional versus ring contacts with respect to local anatomy, active stimulation contact, and over time. Directional contacts display larger impedances than ring contacts. Impedances generally increase slightly over the first year of therapy, save for a transient decrease immediately post-surgery under general anesthesia during pulse generator placement. Local impedances decrease at active stimulation sites, and contacts in closest proximity to internal capsule display higher impedances than other anatomic sites. DBS leads rotate slightly in the immediate postoperative period but otherwise remain stable over the following year. These data provide useful information for setting clinical stimulation parameters over time. (shrink)

This paper studies effective aspects of Jacobson radicals of rings and their applications from the viewpoint of reverse mathematics. First, we propose four radicals of rings, showing that the first order (resp., second order) left and right Jacobson radical coincide in (resp., ). Second, we study Jacobson radicals in left (resp., right) local rings and show that the second order left and right Jacobson radical of left (resp., right) local rings coincide within. Third, we (...) apply our results about Jacobson radicals of rings and local rings to study properties of left (resp., right) strongly indecomposable modules; furthermore, we study effective aspects of typical lemmas and theorems related to strongly indecomposable modules, and show that proves the Fitting Lemma as well as the Krull‐Schmidt‐Azumaya Theorem and that proves the Krull‐Schmidt Theorem. (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)

Let [Formula: see text] be an expansion of either an ordered field [Formula: see text], or a valued field [Formula: see text]. Given a definable set [Formula: see text] let [Formula: see text] be the ring of continuous definable functions from [Formula: see text] to [Formula: see text]. Under very mild assumptions on the geometry of [Formula: see text] and on the structure [Formula: see text], in particular when [Formula: see text] is [Formula: see text]-minimal or [Formula: see text]-minimal, or (...) an expansion of a local field, we prove that the ring of integers [Formula: see text] is interpretable in [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] is definably connected of pure dimension [Formula: see text], then [Formula: see text] defines the subring [Formula: see text]. If [Formula: see text] is [Formula: see text]-minimal and [Formula: see text] has no isolated points, then there is a discrete ring [Formula: see text] contained in [Formula: see text] and naturally isomorphic to [Formula: see text], such that the ring of functions [Formula: see text] which take values in [Formula: see text] is definable in [Formula: see text]. (shrink)

We show that if R is a nonconstant regular (semi-)local subring of a rational function field over an algebraically closed field of characteristic zero, Hilbert's Tenth Problem for this ring R has a negative answer; that is, there is no algorithm to decide whether an arbitrary Diophantine equation over R has solutions over R or not. This result can be seen as evidence for the fact that the corresponding problem for the full rational field is also unsolvable.

A grounded theory study of psychiatric nurses’ experiences of administering medication to involuntary psychiatric patients revealed a basic social process of justifying coercion. Although the 17 nurses interviewed all reported success at avoiding the use of coercion, each had an individual approach to using the nurse-patient relationship to do this. However, all the nurses used the same process to reconcile themselves to using coercion when it became necessary. This has three stages: assessment of need; negotiation; and justifying and taking coercive (...) action. Two critical junctures - decision to engage and impasse - determine the progression from one stage to the next. The process of justifying coercion allows a nurse to engage in behavior generally disapproved of while retaining a self-image of a ‘good’ nurse. (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)