We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.

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)

We prove that there are 2 χ 0 pairwise non elementarily equivalent existentially closed ordered groups, which solve the main open problem in this area (cf. [3, 10]). A simple direct proof is given of the weaker fact that the theory of ordered groups has no model companion; the case of the ordered division rings over a field k is also investigated. Our main result uses constructible sets and can be put in an abstract general framework. Comparison (...) with the standard methods which use forcing (cf. [4]) is sketched. (shrink)

We introduce prime products as a generalization of ultraproducts for positive logic. Prime products are shown to satisfy a version of Łoś’s Theorem restricted to positive formulas, as well as the following variant of the Keisler Isomorphism Theorem: under the generalized continuum hypothesis, two models have the same positive theory if and only if they have isomorphic prime powers of ultrapowers.

This paper is a general introduction to Positive Logic, where only what we call h-inductive sentences are under consideration, allowing the extension to homomorphisms of model-theoric notions which are classically associated to embeddings; in particular, the existentially closed models, that were primitively defined by Abraham Robinson, become here positively closed models. It accounts for recent results in this domain, and is oriented towards the positivisation of Jonsson theories.

We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a group scheme action.

Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector spaces over algebraically (...) closed fields is the model-completion of the theory of vector spaces. (shrink)

A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP generated by a universal classKof finitely subdirectly irreducible algebras such that Γa has the Fraser-Horn property. If ⟦a≠b⟧ ∩ ⟦c≠d⟧ = ∅ is definable inKandKhas a model companion ofK-simple algebras, then it is shown that ISP has a model companion. Conversely, a sufficient condition is given for ISP to have no model companion.

Abstract.In this paper we show that the theory of fields together with an integrally closed subring, the theory of formally real fields with a real holomorphy ring and the theory of formally \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document}-adic fields with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document}-adic holomorphy ring have no model companions in the language of fields augmented by a unary predicate for the corresponding ring.

The variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results [19], it has a model completion. In this article, we supply a finite and rather simple axiomatization of the model completion.

If are structures for a first-order language , is said to be algebraically closed in just in case every positive existential -sentence true in is true in . In 1976 Elliott showed that unital AF algebras are classified up to isomorphism by corresponding dimension groups with order unit. This paper shows that one dimension group with order unit is algebraically closed in another just in case the corresponding AF algebras, viewed as metric structures, fall in the same relation.

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ (...) theories interpretable in existential theories in the process. (shrink)

We point out that the theory of difference fields with algebraically closed fixed field has no model companion.

Lindström’s Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious extension of first order logic with the two model theoretic properties mentioned, namely existential second order logic. We show that existential second order logic has a whole family of proper extensions satisfying the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. Furthermore, we show that in (...) the context of negation-less logics, _positive logics_, as we call them, there is no strongest extension of first order logic with the Compactness Theorem and the Downward Löwenheim-Skolem Theorem. (shrink)

In model theory, a branch of mathematical logic, we can classify mathematical structures based on their logical complexity. This yields the so-called stability hierarchy. Independence relations play an important role in this stability hierarchy. An independence relation tells us which subsets of a structure contain information about each other, for example, linear independence in vector spaces yields such a relation.Some important classes in the stability hierarchy are stable, simple, and NSOP $_1$, each being contained in the next. For each (...) of these classes there exists a so-called Kim-Pillay style theorem. Such a theorem describes the interaction between independence relations and the stability hierarchy. For example, simplicity is equivalent to admitting a certain independence relation, which must then be unique.All of the above classically takes place in full first-order logic. Parts of it have already been generalised to other frameworks, such as continuous logic, positive logic, and even a very general category-theoretic framework. In this thesis we continue this work.We introduce the framework of AECats, which are a specific kind of accessible category. We prove that there can be at most one stable, simple, or NSOP $_1$ -like independence relation in an AECat. We thus recover (part of) the original stability hierarchy. For this we introduce the notions of long dividing, isi-dividing, and long Kim-dividing, which are based on the classical notions of dividing and Kim-dividing but are such that they work well without compactness.Switching frameworks, we generalise Kim-dividing in NSOP $_1$ theories to positive logic. We prove that Kim-dividing over existentially closed models has all the nice properties that it is known to have in full first-order logic. We also provide a full Kim-Pillay style theorem: a positive theory is NSOP $_1$ if and only if there is a nice enough independence relation, which then must be given by Kim-dividing.Abstract prepared by Mark Kamsma.E-mail:[email protected]:https://markkamsma.nl/phd-thesis. (shrink)

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.

The global COVID-19 pandemic has created a crisis of suffering. We conceptualize suffering as a deeply existential issue that fundamentally changes people indelible ways and for which there are no easy solutions. To better understand its effects and how people can flourish in the midst of this crisis, we formally introduce and elaborate on an Existential Positive Psychology Model of Suffering (EPPMS) and apply that to the COVID-19 global pandemic. Our model has three core propositions: (a) suffering reveals (...) existential concerns, (b) existential anxiety impairs one's ability to find meaning, and (c) cultivating meaning is the primary way to address suffering and allay existential anxiety, eventually leading to flourishing (and potentially growth). We apply this model to the COVID-19 pandemic, including how to build meaning, and discuss clinical implications. (shrink)

Bimanual robots have been studied for decades and regulation on internal force of the being held object by two manipulators becomes a research interest in recent years. In this paper, based on impedance model, a method to obtain the optimal target position for bimanual robots to hold an object is proposed. We introduce a cost function combining the errors of the force and the position and manage to minimize its value to gain the optimal coordinates for the robot end (...) effectors. To implement this method, two necessary algorithms are presented, which are the closed-loop inverse kinematics method to work out joint positions from desired EE pose and the generalized-momentum-based external force observer to measure the subjected force acting on the EE so as to properly compensate for the joint torques. To verify the effectiveness, practicality, and adaptivity of the proposed scheme, in the simulation, a bimanual robot system with three degrees of freedom in every manipulator was constructed and employed to hold an object, where the results are satisfactory. (shrink)

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be used (...) with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

Background In June 2016, Canada legalized medical assistance in dying (MAiD). From the outset, some healthcare institutions (including faith-based and non-faith-based hospitals, hospices, and residential aged care facilities) have refused to allow aspects of MAiD onsite, resulting in patient transfers for MAiD assessments and provision. There have been media reports highlighting the negative consequences of these “institutional objections”, however, very little research has examined their nature and impact. Methods This study reports on findings from 48 semi-structured qualitative interviews conducted with (...) MAiD assessors and providers, MAiD team members (working to coordinate care and lead MAiD programs in institutions and health authorities), and family caregivers on their experiences with institutional objection. Participants were recruited from the Canadian provinces of British Columbia, Ontario, and Nova Scotia. Data were analyzed using inductive thematic analysis. Results Themes identified were: (1) basis for institutional objection (with objections commonly rooted in religious values and a particular philosophy of palliative care); (2) scope of objection (demonstrating a wide range of practices objected to); (3) lack of transparency regarding institutional position; (4) impacts on patients; (5) impacts on health practitioners; and (6) catalysts for change. Participants reported that many institutions’ objections had softened over time, lessening barriers to MAiD access and adverse impacts on patients and health practitioners. Participants attributed this positive change to a range of catalysts including advocacy by health practitioners and family members, policymaking by local health authorities, education, and relationship building. Nevertheless, some institutions, particularly faith-based ones, retained strong objections to MAiD, resulting in forced transfers and negative emotional and psychological impacts on patients, family members, and health practitioners. Conclusions This paper adds to the limited evidence base about the impacts of institutional objection and can inform practical and regulatory solutions in Canada and abroad. Reform is needed to minimize the negative impacts on patients, their caregivers, and health practitioners involved in MAiD practice. (shrink)

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases (...) considered the PAC property is first order. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Anthony Close THE EMPIRICAL AUTHOR: SALMAN RUSHDIE'S THE SATANIC VERSES HOBBES, comparing the author ofan action to the owner ofgoods, asserts, "And as the right of possession, is called dominion; so the right of doing any action, is called authority" (Leviathan, Book I, chap. 16). My purpose in this essay is to apply this Hobbesian maxim to the relation Author/Text, expanding somewhat Hobbes's notion of authority. I presuppose that (...) in our day-to-day dealings with our fellow men, we envisage each others' acts as exhibiting purpose and commitment, which make them ours in more than the platitudinous sense that we performed them. By virtue of that, they confer on us a privileged, though clearly not unchallengeable, authority in saying what they are and what they are for. Such, in effect, is the position reached by Austin in How to Do Things with Words, and it broadly corresponds to that of various philosophical writings on human action—by Anscombe, Davidson, and Melden.1 To be sure, we may legitimately consider human behavior from other viewpoints (e.g., structuralist, anthropological, psychoanalytical, Marxist) trained on its unconscious presuppositions. Yet, insofar as such theorizing fails to acknowledge the priority of the Hobbesian perspective, it will seem perverse for a reason that has been well put by Charles Taylor. Precisely because history is made up of purposeful activity, Taylor argues, we need to explain historical patterns in a way that is "intelligible in relation to conscious action" even though they may not "issue from conscious action."2 By this criterion much of our modern literary theory is defective. A vivid measure of the deficiency is provided by the furor over Salman Rushdie's TL· Satanic Verses, culminatingin thefatwa pronounced against Philosophy and Literature, © 1990, 14: 248-267 Anthony Close249 him by the Ayatollah Khomeini in February 1989. I take it that for anyone vocationally committed to the practice or study ofliterature and to the cause of freedom of expression, the defense of Rushdie cannot be a matter of indifference. Nor can one be indifferent to the chasm of misunderstanding that separates Rushdie and his apologists from the novel's Muslim opponents. I believe that these two causes—defending Rushdie and bridging the chasm—can be reconciled by offering better explanations ofhis novel in place ofcrude denunciations or, from some non-Muslim quarters, smug and knowing dismissals. Yet, as we shall see, the task of explanation could be considered hamstrung by our modern poetics. I was reminded ofHobbes's textby Rushdie's lucid and cogent defense of his novel in TL· Independent (London, February 4, 1990). Against the accusations that he had deliberately reviled the Islamic faith, he argued as follows. Though TL· Satanic Verses, like many novels that Rushdie esteems, is a work of radical dissent, questioning, and reimagining, it is motivated by a spirit of serious inquiry rather than debunking derision. More particularly, it reflects a determination that underlies all Rushdie's work: "to create a literary language and literary forms in which the experience offormerly-colonised, still-disadvantaged peoples might find full expression." He continues: "It is written from the very experience of uprooting, disjuncture and metamorphosis... that is the migrant condition, and from which, I believe, can be derived a metaphor for all humanity.... [It] celebrates hybridity, impurity, intermingling, the transformation that comes of new and unexpected combinations of human beings, cultures, ideas, politics, movies, songs. It rejoices in mongrelisation and fears the absolutism of the Pure." Note the insistence on how these themes flow direcdy from Rushdie's own experience. Two days after the publication of this article, Harold Pinter gave on Rushdie's behalf a lecture on the relationship of literature to religion and society at the Institute of Contemporary Arts in London. In this lecture, Rushdie articulated a Bakhtinian view of the novelist's function: to dramatize ironically and noncommittally the clash of voices, languages, and ideologies in a world without gods and without traditionsanctioned truth. Rushdie referred specifically, I think, to a species of postmodernist novel which we may dub "palimpsest history";3 the species includes Rushdie's works, García Márquez's One Hundred Years of Solitude, Carlos Fuentes's Terra Nostra... (shrink)

We introduce a notion of the space of types in positive model theory based on Stone duality for distributive lattices. We show that this space closely mirrors the Stone space of types in the full first-order model theory with negation (Tarskian model theory). We use this to generalise some classical results on countable models from the Tarskian setting to positive model theory.

In the context of continuous logic, this paper axiomatizes both the class \ of lattice-ordered groups isomorphic to C for X compact and the subclass \ of structures existentially closed in \; shows that the theory of \ is \-categorical and admits elimination of quantifiers; establishes a Nullstellensatz for \ and \; shows that \\in \mathcal {C}\) has a prime-model extension in \ just in case X is Boolean; and proves that in a sense relevant to continuous (...) logic, positive formulas admit in \ elimination of quantifiers to positive formulas. (shrink)

A structure is called weakly oligomorphic if its endomorphism monoid has only finitely many invariant relations of every arity. The goal of this paper is to show that the notions of homomorphism‐homogeneity, and weak oligomorphy are not only completely analogous to the classical notions of homogeneity and oligomorphy, but are actually closely related. We first prove a Fraïssé‐type theorem for homomorphism‐homogeneous relational structures. We then show that the countable models of the theories of countable weakly oligomorphic structures are mutually homomorphism‐equivalent (...) (we call first order theories with this property weakly ω‐categorical). Furthermore we show that every weakly oligomorphic homomorphism‐homogeneous structure contains (up to isomorphism) a unique homogeneous, homomorphism‐homogeneous core, to which it is homomorphism‐equivalent. As a consequence we obtain that every countable weakly oligomorphic structure is homomorphism‐equivalent to a finite or ω‐categorical structure. As a corollary we obtain a characterization of positive existential theories of weakly oligomorphic structures as the positive existential parts of ω‐categorical theories. (shrink)

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions. Let $N$ be a countable saturated model of some complete theory $T$ , and let $(N,\sigma)$ denote an expansion of (...) $N$ to the signature $L_{0}$ which is a model of some universal theory $T_{0}$ . We prove that when all existentially closed models of $T_{0}$ have the same existential theory, $(N,\sigma)$ is Truss generic if and only if $(N,\sigma)$ is an e-atomic model. When $T$ is $\omega$ -categorical and $T_{0}$ has a model companion $T_{\mathrm {mc}}$ , the e-atomic models are simply the atomic models of $T_{\mathrm {mc}}$. (shrink)

Acknowledging separable factors underlying negative symptoms may lead to better understanding and treatment of negative symptoms in individuals with schizophrenia. The current study aimed to test whether the negative symptoms factor (NSF) of the Positive and Negative Syndrome Scale (PANSS) would be better represented by expressive and experiential deficit factors, rather than by a single factor model, using confirmatory factor analysis (CFA). Two hundred and twenty individuals with schizophrenia spectrum disorders completed the PANSS; subsamples additionally completed the Brief Negative (...) Symptom Scale (BNSS) and the Motivation and Pleasure Scale—Self-Report (MAP-SR). CFA results indicated that the two-factor model fit the data better than the one-factor model; however, latent variables were closely correlated. The two-factor model’s fit was significantly improved by accounting for correlated residuals between N2 (emotional withdrawal) and N6 (lack of spontaneity and flow of conversation), and between N4 (passive social withdrawal) and G16 (active social avoidance), possibly reflecting common method variance. The two NSF factors exhibited differential patterns of correlation with subdomains of the BNSS and MAP-SR. These results suggest that the PANSS NSF would be better represented by a two-factor model than by a single-factor one, and support the two-factor model’s adequate criterion-related validity. Common method variance among several items may be a potential source of measurement error under a two-factor model of the PANSS NSF. (shrink)

In this paper, we study bounded versions of some model-theoretic notions and results. We apply these results to the context of models of bounded arithmetic theories as well as some related complexity questions. As an example, we show that if the theory \(\rm S_2 ^1(PV)\) has bounded model companion then \(\rm NP=coNP\). We also study bounded versions of some other related notions such as Stone topology.

Background Voluntary assisted dying became lawful in Victoria, the first Australian state to permit this practice, in 2019 via the Voluntary Assisted Dying Act 2017 (Vic). While conscientious objection by individual health professionals is protected by the Victorian legislation, objections by institutions are governed by policy. No research has been conducted in Victoria, and very little research conducted internationally, on how institutional objection is experienced by patients seeking assisted dying. Methods 28 semi-structured interviews were conducted with 32 family caregivers and (...) one patient about the experience of 28 patients who sought assisted dying. Participants were interviewed during August-November 2021. Data from the 17 interviews (all with family caregivers) which reported institutional objection were analysed thematically. Results Participants reported institutional objection affecting eligibility assessments, medication access, and taking the medication or having it administered. Institutional objection occurred across health settings and was sometimes communicated obliquely. These objections resulted in delays, transfers, and choices between progressing an assisted dying application and receiving palliative or other care. Participants also reported objections causing adverse emotional experiences and distrust of objecting institutions. Six mediating influences on institutional objections were identified: staff views within objecting institutions; support of external medical practitioners and pharmacists providing assisted dying services; nature of a patient’s illness; progression or state of a patient’s illness; patient’s geographical location; and the capability and assertiveness of a patient and/or caregiver. Conclusions Institutional objection to assisted dying is much-debated yet empirically understudied. This research found that in Victoria, objections were regularly reported by participants and adversely affected access to assisted dying and the wider end-of-life experience for patients and caregivers. This barrier arises in an assisted dying system that is already procedurally challenging, particularly given the limited window patients have to apply. Better regulation may be needed as Victoria’s existing policy approach appears to preference institutional positions over patient’s choice given existing power dynamics. (shrink)

In this paper we give a differential lifting principle which provides a general method to geometrically axiomatize the model companion (if it exists) of some theories of differential topological fields. The topological fields we consider here are in fact topological systems in the sense of van den Dries, and the lifting principle we develop is a generalization of the geometric axiomatization of the theory DCF₀ given by Pierce and Pillay. Moreover, it provides a geometric alternative to the axiomatizations obtained (...) by Tressl and Guzy/Point in separate papers where the authors also build general schemes of axioms for some model complete theories of differential fields. We first characterize the existentially closed models of a given theory of differential topological fields and then, under an additional hypothesis of largeness, we show how to modify this characterization to get a general scheme of first-order axioms for the model companion of any large theory of differential topological fields. We conclude with an application of this lifting principle proving that, in existentially closed models of a large theory of differential topological fields, the jet-spaces are dense in their ambient topological space. (shrink)

This paper introduces a new theory of constant regions, which generalizes that of interstices, in nonstandard models of arithmetic. In particular, we show that two homogeneity notions introduced by Richard Kaye and the author, namely, constantness and pregenericity, are equivalent. This led to some new characterizations of generic cuts in terms of existential closedness.

The Guarded Negation Fragment (GNFO) is a fragment of first-order logic that contains all positive existential formulas, can express the first-order translations of basic modal logic and of many description logics, along with many sentences that arise in databases. It has been shown that the syntax of GNFO is restrictive enough so that computational problems such as validity and satisfiability are still decidable. This suggests that, in spite of its expressive power, GNFO formulas are amenable to novel optimizations. In this (...) article we study the model theory of GNFO formulas. Our results include effective preservation theorems for GNFO, effective Craig Interpolation and Beth Definability results, and the ability to express the certain answers of queries with respect to a large class of GNFO sentences within very restricted logics. (shrink)

The COVID-19 pandemic has had a widespread effect on the thoughts, emotions and behavior of millions of people all around the world. In this context, a large body of scientific literature examining the mental health impact of this global crisis has emerged. The majority of these studies have framed this impact in terms of pre-defined categories derived from psychiatric nosology, such as anxiety disorders, depression or post-traumatic stress disorder. These constructs often fail to capture the complexity of the actual experiences (...) of the individuals being studied; more specifically, they describe these experiences exclusively in terms of disease, while neglecting their potentially adaptive or “salutogenic” aspects. Similarly, discussion of psychological assistance for these individuals has largely been confined to a reiteration of “evidence-based” psychological or pharmacological techniques which can be delivered using remote access technology. In the context of the COVID-19 pandemic, these approaches are likely to be of mixed efficacy. Conversely, “negative emotions” or distressing psychological experiences may actually be functional in the setting of a disaster or crisis, serving to minimize harm, maximize social coherence and compliance, and facilitate adherence to safety measures. The limitations of the “conventional” approach are, to a certain degree, inherent to the prevailing medical model of mental health. Beyond these considerations lies the concept of “salutogenesis,” a term which refers to the innate capacity of individuals to create and maintain health and well-being in the face of adversity. Using principles derived from the second wave of positive psychology, particularly its emphasis on the totality of human experience and the possibility of deriving meaning and character growth from suffering, this paper conceptually analyses the relevant aspects of salutogenesis and PP2.0, and proposes an alternate approach for addressing mental health concerns during the COVID-19 pandemic. Such an approach, while acknowledging the utility of the conventional medical-psychotherapeutic model in specific cases, reduces the risk of medicalizing human experience, and provides individuals and communities with opportunities for growth and adaptation. The benefits of this proposal could potentially extend far beyond the current crisis, offering an opportunity for the field of psychiatry and mental health research to move away from a purely “disease-centered” model. (shrink)

We show that the quantifier elimination result for the Shelah-Spencer almost sure theories of sparse random graphs $$G(n,n^{-\alpha })$$ given by Laskowski (Isr J Math 161:157–186, 2007) extends to their various analogues. The analogues will be obtained as theories of generic structures of certain classes of finite structures with a notion of strong substructure induced by rank functions and we will call the generics Baldwin–Shi hypergraphs. In the process we give a method of constructing extensions whose ‘relative rank’ is negative (...) but arbitrarily small in context. We give a necessary and sufficient condition for the theory of a Baldwin–Shi hypergraph to have atomic models. We further show that for certain well behaved classes of theories of Baldwin–Shi hypergraphs, the existentially closed models and the atomic models correspond. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Close Enemies: The Relationship of Psychiatry and Psychology in the Assessment of Mental DisordersPhilippe Le Moigne, PhDAs Peter Zachar rightly points out in his comment, the assessment of mental disorders underwent new developments with the release of the Diagnostic and Statistical Manual of Mental Disorders-V in 2013 (American Psychiatric Association, 2013). Whereas in 1980, the manual had been thought of in a rigorously categorical way, on the basis of (...) distinct and closed syndromic entities, this new version advocated the development of a radically dimensionalist approach, with the diagnosis aiming this time to restore the whole symptomatological picture of the patient on a spectrum of ratings are supposed to cover the entirety of psychiatric semiology (American Psychiatric Association, 2013).For its part, my article aimed to show how standardized assessment, guided by the return of psychiatry’s authority and the assertion of its legitimacy in the diagnostic field, gave the ascendancy in the 1980s to the classificatory tradition and thus to the categorical model, to the detriment of personality approach and test psychology which offered a competing solution here. This perspective, historically dated, may have led the reader to think that there is an antagonism that cannot be overcome here. Rather, it should be seen as a form of structuring opposition, or even a “complementarity inscribed in rivalry,” between psychiatry and psychology, which is naturally susceptible to change over time.Indeed, the reversal operated by the Diagnostic and Statistical Manual of Mental Disorders-V is not total because it cannot be total. The defense of the dimensionalist approach, dear to the psychological testing tradition, was intended here to allow the identification of co-morbidities, present in most patients but poorly apprehended by the categorical approach, and to open up diagnosis to prevention by screening for minor manifestations of psychopathology when they suggest the [End Page 259] development of a manifest episode of the disease in the more or less long term. The risk here is that we end up with overdiagnosis and thus an over-representation of false positives (Wakefield, 2015). In other words, this type of approach does not escape the obligation to determine threshold scores, likely to indicate the lower limit of the disorder, and thus to resort to a categorical approach. There is a first affinity between the two perspectives which obeys, beyond the divergences in principle, a technical requirement.But the two approaches have even more in common when we look at their epistemological background: they share the idea that the representation and the intervention on mental disorder, to use Ian Hacking’s expression (1983), must be based on the model proposed by the physical and natural sciences. And as Greta Kaluzeviciute aptly points out in her comment, this orientation leads to the idea of measuring mental disorder in particular to conduct elaborate quantification operations to determine, for example, whether two entities are statistically distinct or whether a drug has a significant effect on the evolution of a pathology.This is in fact an old question that can be formulated as follows, to use the expression of the psychometrician Joel Michell (1999): are psychological dimensions metric? In other words, if we want to apply the language of numbers to mental disorders, they must share its properties, two of which seem essential: it must be possible to establish that each mental disorder, in the same way as qualities attributable to length for example, has a zero and can be divided by means of gradients (or degrees of intensity) whose interval is constant (Le Moigne, 2018; Michell, 1999). For lack of space, let us only address the second condition. This one has already been denied by many, starting with Bergson at the end of the nineteenth century (1889). He does not believe in the quantification of psychological expressions, starting with sensations. What is the common point, he wrote, between the feeling of a mild pain, as one feels a stiffness, and the sensation of a needle being hammered into your flesh? For him, one and the other of these intensities are incomparable, so that they do not belong to a similar register of sensations that one could stage from a 0 toward a... (shrink)

Van Gelder has presented a position which he ties closely to a broad class of models known as dynamical models. While supporting many of his broader claims about the importance of this class (as has been argued by connectionists for quite some time), I note that there are a number of unique characteristics of his brand of dynamicism. I suggest that these characteristics engender difficulties for his view.

We compare bifocal stance theory's (BST) approach to social learning to construal level theory's (CLT) – a social-cognitive theory positing that psychological closeness to a model influences action-representation and thus modulates how concretely or abstractly observers emulate models. Whereas BST argues that social motives produce higher fidelity emulation, CLT argues that psychological closeness impacts cognitive construal and produces more concrete emulation across diverse motivations for emulation.

Abstract: Kant follows a substantial tradition by defining judgment so that it must involve a relation of concepts, which raises the question of why he thinks that single-term existential judgments should still qualify as judgments. There is a ready explanation if Kant is somehow anticipating a Fregean second-order account of existence, an interpretation that is already widely held for separate reasons. This paper examines Kant's early (1763) critique of Wolffian accounts of existence, finding that it provides the key idea in (...) his mature model of existential judgment, which is in fact sharply opposed to the Fregean strategy. By relating this to Kant's theory of judgment in general—in particular, to his claim for an isomorphism between the assertoric function of judgment and the category of existence—a preliminary case is made that absolute positing, far from being a marginal special case, accomplishes the primary function of judgment. This argument shows the importance of distinguishing between contexts in which Kant is treating judgment as a vehicle for inference (e.g. pure general logic) and contexts in which he is treating it, more robustly, as the cognition of an object. (shrink)

The ongoing COVID-19 pandemic has taken a significant toll on mental health; people around the world are experiencing high levels of stress and deteriorated wellbeing. The past research shows that positive emotions can help people cultivate a resilient mindset; however, the reality created by the global crisis itself limits the opportunities for experiencing positive emotions. Thus, it is unclear to what extent their effect is strong enough to counter the psychological impact of the current pandemic. Here, the author reports the (...) findings of a survey conducted across two large representative samples in the United Kingdom and the United States during the first wave of the COVID-19 pandemic. A linear regression model revealed that the presence of positive emotions is strongly linked with resilience, in particular for individuals experiencing more negative emotions. These results show that positive emotions are particularly important to mental health in the context of high stress, reflected by increased levels of negative emotional experiences. These results are also consistent with the existential positive psychology perspective, which posits that even negative emotions can contribute to wellbeing once they are transformed. The author discusses the potential of positive emotions to transform suffering and thereby ameliorate the negative impact of the present collective crisis. (shrink)

After having briefly discussed the question of whether Kierkegaard can be considered as a “philosopher of religion,” this chapter deals with three classic topics of religious philosophy: faith and reason; the existence of God; and the immortality of the soul. As regards the first question, an attempt will be made to show that Kierkegaard's position is not a kind of theological gnoseology, but an original kind of existential philosophy. It will be pointed out that although reason is a negative condition (...) for faith, still faith is in no way a kind of knowledge, but a proper way of existence. Regarding the second issue, Kierkegaard's apophatical theology and his argumentation against traditional natural theology will be treated in connection with the general problem of the (un)demonstrability of existential assertions. Finally, the chapter will outline that, for Kierkegaard, immortality is not a metaphysical quality of the soul, but an existential possibility that is closely connected with becoming a self of an existing individual. (shrink)

The following paper explicates and critically analyses the existential ethics of the reflective postmodernist phase in the work of Agnes Heller. Beginning with a brief summary of the biographical and theoretical roots of her development, it goes on to analyse the meaning of her key slogan of ?turning contingency into destiny.? After elaborating her version of the ?existential leap? and her later attempts to refine her position in An Ethics of Personality, the paper will employ some literary lives from W. (...) G. Sebald and J. M. Coetzee to test the general viability of Heller's model. (shrink)

This paper studies the problems of tip position regulation and vibration suppression of flexible manipulators without using the model. Because of the two-timescale characteristics of flexible manipulators, applying the existing model-free control methods may lead to ill-conditioned numerical problems. In this paper, the dynamics of a flexible manipulator is decomposed into two subsystems which are linear and controllable at different timescales by singular perturbation theory and a model-free composite controller is designed to alleviate the ill-conditioned numerical problems. (...) To do this, a model-free composite control strategy is constructed which facilitates in designing the controller in slow and fast timescales. In the slow timescale, the slow subsystem controller is designed by adaptive dynamic programming based on the measurements of the slow inputs and the position, while the vibration in the slow timescale is estimated by the least square method. In the fast timescale, the vibration is reconstructed based on the measurements of vibration and its estimate in the slow timescale, by which the fast controller is designed using ADP. Stability of the closed-loop system is proved by SP theory. Finally, simulations are given to show the feasibility and effectiveness of the proposed methods. (shrink)

The complex hexaploid wheat genome offers many challenges for genomics research. Expressed sequence tags facilitate the analysis of gene-coding regions and provide a rich source of molecular markers for mapping and comparison with model organisms. The objectives of this study were to construct a high-density EST chromosome bin map of wheat homoeologous group 2 chromosomes to determine the distribution of ESTs, construct a consensus map of group 2 ESTs, investigate synteny, examine patterns of duplication, and assess the colinearity with (...) rice of ESTs assigned to the group 2 consensus bin map. A total of 2600 loci generated from 1110 ESTs were mapped to group 2 chromosomes by Southern hybridization onto wheat aneuploid chromosome and deletion stocks. A consensus map was constructed of 552 ESTs mapping to more than one group 2 chromosome. Regions of high gene density in distal bins and low gene density in proximal bins were found. Two interstitial gene-rich islands flanked by relatively gene-poor regions on both the short and long arms and having good synteny with rice were discovered. The map locations of two ESTs indicated the possible presence of a small pericentric inversion on chromosome 2B. Wheat chromosome group 2 was shown to share syntenous blocks with rice chromosomes 4 and 7. (shrink)

The popularity of the stakeholder model has been achieved thanks to its powerful visual scheme and its very simplicity. Stakeholder management has become an important tool to transfer ethics to management practice and strategy. Nevertheless, legitimate criticism continues to insist on clarification and emphasises on the perfectible nature of the model. Here, rather than building on the discussion from a philosophical or theoretical point of view, a different and innovative approach has been chosen: the analysis will return to (...) the origin of stakeholder theory and will keep the graphical framework firmly in perspective. It will confront the stakeholder model’s graphical representation to the discussion on stakeholder definition, stakeholder identification and categorisation, to re-centre the debate to the strategic origin of the stakeholder model. The ambiguity and the vagueness of the stakeholder concept are discussed from managerial and legal approaches. The impacts of two major shortcomings of the popular stakeholder framework are examined: the boundaries and the level of the firm’s environment, and the ambivalent position of pressure groups and regulators. Working pragmatically, with a focus on the managerial and organisational perspective, an attempt is made to clarify the categorisations and classifications by introducing new terminology with a distinction between stakeholders, stakewatchers and stakekeepers. The analysis will finally lead to a proposed upgraded and refined version of the stakeholder model, with incremental ameliorations close to Freeman’s original model and a return of focus to its essence, the managerial implications in a strategic approach. (shrink)

We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B 2 of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B 2. The axioms of Schmid [7], [8] for the AC and EC members of B 2 are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of (...) Clark and Davey [3] for B 2 and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B 2, this method transfers the entire discussion into an equivalent dual category X 2 of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X 2 prove to be much more readily constructed and analyzed than the corresponding algebras in B 2. (shrink)

There is growing international interest in the choice of socioeconomic indicators for health research. This study used a combination of standard and novel methods to compare three occupation-based measures of social position in terms of their ability to explain variation and measure inequality in self-assessed health. The recently developed National Statistics Socioeconomic Classification (NS-SEC) is compared with its predecessor, the Registrar General64 living in private households in Scotland, logistic regression models are used to compare the classifications' ability to predict self-assessed (...) health. Concentration indices are estimated to compare how well they capture inequality in self-assessed health. The study shows that all three classifications are strongly associated with self-assessed health, though the associations are heavily attenuated by adjustment for one another and for other measures of social position. Despite their differing theoretical bases, the three are closely related. No evidence is found that any of them systematically under- or overstate the extent of inequality in self-assessed health in either men or women, and the extent to which they measure independent dimensions of social inequality is questioned. It is concluded that the availability of the new classifications is unlikely to transform our understanding of the extent or the causes of socioeconomic inequality in health, but provides useful opportunities for sensitivity analysis. (shrink)