Let T be superstable. We say a type p is weakly minimal if R(p, L, ∞) = 1. Let $M \models T$ be uncountable and saturated, H = p(M). We say $D \subset H$ is locally modular if for all $X, Y \subset D$ with $X = \operatorname{acl}(X) \cap D, Y = \operatorname{acl}(Y) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). Theorem 1. Let p ∈ S(A) be weakly (...) minimal and D the realizations of $\operatorname{stp}(a/A)$ for some a realizing p. Then D is locally modular or p has Morley rank 1. Theorem 2. Let H, G be definable over some finite A, weakly minimal, locally modular and nonorthogonal. Then for all $a \in H\backslash\operatorname{acl}(A), b \in G\operatorname{acl}(A)$ there are a' ∈ H, b' ∈ G such that $a' \in \operatorname{acl}(abb' A)\backslash\operatorname{acl}(aA)$ . Similarly when H and G are the realizations of complete types or strong types over A. (shrink)

In [R. Vaught, Denumerable models of complete theories, in: Infinitistic Methods, Pregamon, London, 1961, pp. 303–321] Vaught conjectured that a countable first order theory has countably many or 20 many countable models. Here, the following special case is proved.

Suppose T is superstable. Let ≤ denote the fundamental order on complete types, [ p] the class of the bound of p, and U(--) Lascar's foundation rank (see [LP]). We prove THEOREM 1. If $q and there is no r such that $q , then U(q) + 1 = U(p). THEOREM 2. Suppose $U(p) and $\xi_1 is a maximal descending chain in the fundamental order with ξ κ = [ p]. Then k = U(p). That the finiteness of U(p) in (...) Theorem 2 is necessary follows from THEOREM 3. There is an ω-stable theory with a type p ∈ S 1 (φ) such that (1) U(p) = ω + 1, and (2) there is a maximal descending chain of proper extensions of [ p] which has order type ω. (shrink)

Theorem A. Let T be a small superstable theory, A a finite set, and ψ a weakly minimal formula over A which is contained in some nontrivial type which does not have Morley rank. Then ψ is contained in some nonalgebraic isolated type over A. As an application we prove Theorem B. Suppose that T is small and superstable, A is finite, and there is a nontrivial weakly minimal type p ∈ S(A) which does not have Morley rank. Then the (...) prime model over A is not minimal over A. (shrink)

In this paper a class of simple theories, called the low theories is developed, and the following is proved. Theorem. Let T be a low theory. A set and a, b elements realizing the same strong type over A. Then, a and b realized the same Lascar strong type over A.

Let D be a strongly minimal set in the language L, and $D' \supset D$ an elementary extension with infinite dimension over D. Add to L a unary predicate symbol D and let T' be the theory of the structure (D', D), where D interprets the predicate D. It is known that T' is ω-stable. We prove Theorem A. If D is not locally modular, then T' has Morley rank ω. We say that a strongly minimal set D is pseudoprojective (...) if it is nontrivial and there is a $k < \omega$ such that, for all a, b ∈ D and closed $X \subset D, a \in \mathrm{cl}(Xb) \Rightarrow$ there is a $Y \subset X$ with a ∈ cl(Yb) and |Y| ≤ k. Using Theorem A, we prove Theorem B. If a strongly minimal set D is pseudoprojective, then D is locally projective. The following result of Hrushovski's (proved in $\S4$ ) plays a part in the proof of Theorem B. Theorem C. Suppose that D is strongly minimal, and there is some proper elementary extension D1 of D such that the theory of the pair (D1, D) is ω1-categorical. Then D is locally modular. (shrink)

The main results in the paper are the following. Theorem A. Suppose that T is superstable and M ⊂ N are distinct models of T eq . Then there is a c ϵ N⧹M such that t is regular. For M ⊂ N two models we say that M ⊂ na N if for all a ϵ M and θ such that θ ≠ θ , there is a b ∈ θ ⧹ acl . Theorem B Suppose that T is (...) superstable , M ⊂ na N are models of T eq , and p is a regular type non-orthogonal to t . Then there is a c ϵ N such that t is regular and non-orthogonal to p. Furthermore, there is a formula θ ∈ t such that a ∈ θ and t ⊥ ̷ p ⇒ t is regular. We used these results to obtain ‘good’ tree decompositions of models in superstable theories with NDOP. See Definition 5.1 for the undefined terms. Theorem C Suppose that T is superstable with NDOP and M ⊨ T eq . Then every ⊂ na - decomposition inside M extends to a ⊂ na -decomposition of M. Furthermore, if 〈N η , a η : η ∈ I〉 is any ⊂ na -decomposition of M, then M is minimal over ∪N η and for all η ∈ I. M is dominated by ∪N η over N η . Using some stable group theory we show that when Th is superstable with NDOP and 〈 N η : η ∈ I 〉 is a tree decomposition of M, then M is constructible over ∪ n η with respect to a very strong isolation relation. (shrink)

Suppose $D \subset M$ is a strongly minimal set definable in M with parameters from C. We say D is locally modular if for all $X, Y \subset D$ , with $X = \operatorname{acl}(X \cup C) \cap D, Y = \operatorname{acl}(Y \cup C) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). We prove the following theorems. Theorem 1. Suppose M is stable and $D \subset M$ is strongly minimal. (...) If D is not locally modular then in M eq there is a definable pseudoplane. (For a discussion of M eq see [M, § A].) This is the main part of Theorem 1 of [Z2] and the trichotomy theorem of [Z3]. Theorem 2. Suppose M is stable and $D, D' \subset M$ are strongly minimal and nonorthogonal. Then D is locally modular if and only if D' is locally modular. (shrink)

Theorem A. Suppose that T is superstable and p is a nontrivial type of U-rank 1. Then R(p, L, ∞) = 1. Theorem B. Suppose that T is totally transcendental and p is a nontrivial type of U-rank 1. Then p has Morley rank 1.

The main result is Vaught's conjecture for weakly minimal, locally modular and non-ω-stable theories. The more general results yielding this are the following. THEOREM A. Suppose that T is a small unidimensional theory and D is a weakly minimal set, definable over the finite set B. Then for all finite $A \subset D$ there are only finitely many nonalgebraic strong types over B realized in $\operatorname{acl}(A) \cap D$ . THEOREM B. Suppose that T is a small, unidimensional, non-ω-stable theory such (...) that the universe is weakly minimal and locally modular. Then for all finite A there is a finite $B \subset \mathrm{cl}(A)$ such that a ∈ cl(A) iff a ∈ cl(b) for some b ∈ B. Recall the property (S) defined in the abstract of [B1]. THEOREM C. Let T be as in Theorem B. Then, if T does not satisfy (S), T has 2 ℵ 0 many countable models. Combining Theorem C and the results in [B1] we obtain Vaught's conjecture for such theories. (shrink)

We prove that every relation-universal model of an ω-stable theory is saturated. We also show there is a large class of ω-stable theories for which every resplendent model is homogeneous.

We prove that if every uncountable model of a first-order theory T is ω-saturated and T is superstable then T is categorical in some infinite power.

Theorem A. Let M be a left R-module such that Th(M) is small and weakly minimal, but does not have Morley rank 1. Let $A = \mathrm{acl}(\varnothing) \cap M$ and $I = \{r \in R: rM \subset A\}$ . Notice that I is an ideal. (i) F = R/I is a finite field. (ii) Suppose that a, b 0 ,...,b n ∈ M and a b̄. Then there are s, r i ∈ R, i ≤ n, such that sa + (...) ∑ i ≤ n r ib i ∈ A and $s \not\in I$ . It follows from Theorem A that algebraic closure in M is modular. Using this and results in [B1] and [B2], we obtain Theorem B. Let M be as in Theorem A. Then Vaught's conjecture holds for Th(M). (shrink)

Certain basic concepts of geometrical stability theory are generalized to a class of closure operators containing algebraic closure. A specific case of a generalized closure operator is developed which is relevant to Vaught's conjecture. As an application of the methods, we prove THEOREM A. Let G be a superstable group of U-rank ω such that the generics of G are locally modular and Th(G) has few countable models. Let G - be the group of nongeneric elements of G, G + (...) = G o + G - . Let Π= {q ∈ S( $\emptyset$ ): U(q) $A \subset M$ such that M is almost atomic over A ∪ (G + ∩ M) $\cup \bigcup_{p\in \Pi}$ p(M). (shrink)

We present a self-contained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah's 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.

This article addresses a countermovement to the animal liberation movement and its campaigns against vivisection, factory farming, and recreational hunting in the United States, the United Kingdom, and Australia. As moderate welfarists, pragmatic animal liberationists , and radical abolitionists who advocate animal rights, animal protectionists campaign for animals. The countermovement defends acts that animal protectionists decry. Meanwhile, sociologists accord little study to interplay between the movements . In Buechler's and Cylke's collection of 34 papers on social movements , only one (...) paper focused on countermovements, describing the connection between social movement and countermovement as "a continuous dialect of social change" . Although extensive writings exist on the main campaigns of the animal liberation movement, little scholarly material exists on the defenses mounted by the countermovement. This article examines key elements of a values war, a struggle over moral capital waged by animal protectionists and their countermovement opponents. (shrink)

If there is any social organization that has provided a powerful illustration of the permeable boundaries between social politics—defined by Stephen M. Buechler as “forms of collective action that challenge power relations without an explicit focus on the state”—and social movements , and the role of collective identity in transforming either, as defined for women by Betty Friedan—it would be the Israeli kibbutz movement. The research presented here on grassroots Israeli women activists, a significant proportion of whom had grown up (...) or had lived in a kibbutz, suggests that the social politics of everyday life on a kibbutz facilitated women's participation in larger social movements for peace, but also placed constraints on their activism. Many of these women had left or were in the process of leaving the kibbutz between 1989 and 1999, when this research was conducted. Those who had already left, and anchor women who organized urban demonstrations, saw the kibbutz as a conservative anti-woman force. Nonetheless, evidence gathered from qualitative interviewing with them suggests that the kibbutzim supported women who were politically active on national issues. Several women-led social protest movements illustrate how the kibbutz geared its members to think about the interplay of the moral and social orders in the small spaces of everyday life. (shrink)

In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields with commuting automorphisms are closely related to difference fields. Some authors define a difference ring (or field) as a ring (or field) together with several commuting endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, the model companion of difference fields with one automorphism. Our fields with commuting automorphisms generalize this setting. We have (...) several automorphisms and they are required to commute. Hrushovski has proved that in the case of fields with two or more commuting automorphisms, the existentially closed models do not necessarily form a first order model class. In the present paper, we introduce FCA-classes, an AEC framework for studying the existentially closed models of the theory of fields with commuting automorphisms. We prove that an FCA-class has AP and JEP and thus a monster model, that Galois types coincide with existential types in existentially closed models, that the class is homogeneous, and that there is a version of type amalgamation theorem that allows to combine three types under certain conditions. Finally, we use these results to show that our monster model is a simple homogeneous structure in the sense of S. Buechler and O. Lessman (this is a non-elementary analogue for the classification theoretic notion of a simple first order theory). (shrink)

Background: Increasing collaboration between industrialised and developing countries in human research studies has led to concerns regarding the potential exploitation of resource deprived countries. This study, commissioned by the former National Bioethics Advisory Commission of the United States, surveyed developing country researchers about their concerns and opinions regarding ethical review processes and the performance of developing country and US international review boards .Methods: Contact lists from four international organisations were used to identify and survey 670 health researchers in developing countries. (...) A questionnaire with 169 questions explored issues of IRB review, informed consent, and recommendations.Results: The majority of the developing country researchers were middle aged males who were physicians and were employed by educational institutions, carrying out research on part time basis. Forty four percent of the respondents reported that their studies were not reviewed by a developing country IRB or Ministry of Health and one third of these studies were funded by the US. During the review process issues such as the need for local language consent forms and letters for approval, and confidentiality protection of participants were raised by US IRBs in significantly higher proportions than by host country IRBs.Conclusion: This survey indicates the need for the ethical review of collaborative research in both US and host countries. It also reflects a desire for focused capacity development in supporting ethical review of research. (shrink)

Can we respond to injustices in the world in ways that do more than just address their consequences? In this book, Brooke A. Ackerly argues that what to do about injustice is not just an ethical or moral question, but a political question about assuming responsibility for injustice. Ultimately, Just Responsibility offers a theory of global injustice and political responsibility that can guide action.

From the diverse work and often competing insights of women's human rights activists, Brooke Ackerly has written a feminist and a universal theory of human rights that bridges the relativists' concerns about universalizing from particulars and the activists' commitment to justice. Unlike universal theories that rely on shared commitments to divine authority or to an 'enlightened' way of reasoning, Ackerly's theory relies on rigorous methodological attention to difference and disagreement. She sets out human rights as at once a research ethic, (...) a tool for criticism of injustice and a call to recognize our obligations to promote justice through our actions. This book will be of great interest to political theorists, feminist and gender studies scholars and researchers of social movements. (shrink)

The issue of sexual relations between spouses is a major cause of broken homes in Nigeria and Christian couples are not an exception. People believe that a large percentage of broken homes have the root of their problem traced to sex. The preponderance of broken homes notwithstanding, most studies in this area have been from the socio-scientific and medical cum psychological point of view and many more have focused on teenagers and young people to the exclusion of married couples that (...) need healing in this regard. This article is aimed at bringing out biblical instruction concerning the issue of sex that could help to restore peace to many homes at the verge of breaking down. The focal passage is 1 Corinthians 7:1–5, which was Paul’s instructions to the Corinthian church when they faced a similar problem. This article is an exegetical analysis of the passage and is read rhetorically with the Nigerian situation in mind. It concludes that sex must be enjoyed within the ambits of marriage and within this ambit, the only reason for abstinence is mutual agreement for the purpose of prayer.Contribution: The article upholds gender equality in initiating and enjoying sex and rejects looking down on women who request sex. It also calls for the eradication of female genital mutilation, a tradition based on making women not enjoy sex. (shrink)

The Report of the Ad Hoc Adivisory Group on the Operation of NHS Research Ethics Committees has resulted in a strange mixture of the timid, the revolutionary, and the bizarre.The Report of the Ad Hoc Advisory Group on the Operation of NHS Research Ethics Committees is a curious document.1 The remit of the review was focused on the workings and effectiveness of NHS research ethics committees and the multicentre committees ). The Group was primarily set up in response to a (...) series of complaints from medical researchers about the new research governance regime in the UK as a result of the Clinical Trials Directive2 and the Governance Arrangements for NHS Research Ethics Committees.3 The opportunity was also taken to consider the role of research ethics committees in a wider context, and take account of recent developments in relation to the ethics review of social care research,4 student projects,5 as well as recent legislation such as the Human Tissue Act,6 and the Mental Capacity Act.7 However, the resulting report is a strange mixture of the timid, the revolutionary, and the bizarre.A good example of the report’s timidity is its reluctance to propose fundamental change to the process of review or seriously limit the type of research that requires REC review. To its credit AHAG does suggest that some research ‘especially surveys and many studies on NHS staff, could normally be conducted safely without a requirement for REC review’ .1 This is, of course, to be welcomed. However, the report ultimately seems dismissive of the general complaint from researchers that the current process is inappropriately uniform. For example, in section 3.2, it is argued that the ‘common perception that the NHS REC system is dominated …. (shrink)

El artículo expone dos visiones acerca de la legitimidad del castigo en contextos de exclusión social. En la primera parte, uno de los autores defiende la idea de que los Estados que incumplen con obligaciones legales previas no pueden inculpar a quienes cometan delitos vinculados con ese incumplimiento. No pueden hacerlo porque no tienen el estatus moral para hacerlo de acuerdo a dos objeciones: la de complicidad y la de hipocresía. En la segunda parte, la segunda autora critica esta solución (...) al sostener que la falta de reciprocidad que caracteriza a la relación política vuelve inaplicables las objeciones de hipocresía y complicidad al ámbito del castigo penal estatal. (shrink)

The analysis presented in this article shows that overarching conceptual systems, such as the metaphor “NATIONS ARE A FAMILY,” often bring together expressions with dissimilar intentions, ideologic...

Serving as a healthcare worker in a conflict zone is an experience that is characterized by peculiar and unimaginable challenges. This commentary is an exposition on twelve collated stories of healthcare providers currently serving or who have previously served in war. The stories bring to bear the heaviness of emotions such as fear and guilt that the authors grappled with, while concurrently showing that they embody virtues such as altruism, self-sacrifice, courage, and solidarity. In these stories, we see highlighted recurrent (...) ethical themes including the tension between the duty to others and the duty to self, prioritization and allocation of scarce health resources, ethics of research in war, ethics of virtue and the lasting effects of war. This commentary thus explores and heightens our awareness of the interplay between personal morals and the translation of these into ethics of healthcare provision in war. In so doing, the commentary urges us to reflect on ways by which we can engage the discourse pertaining to war and healthcare ethics. (shrink)

Objective To determine the attitudes of Egyptian patients regarding their participation in research and with the collection, storage and future use of blood samples for research purposes. Design Cross-sectional survey. Study population Adult Egyptian patients (n=600) at rural and urban hospitals and clinics. Results Less than half of the study population (44.3%) felt that informed consent forms should provide research participants the option to have their blood samples stored for future research. Of these participants, 39.9% thought that consent forms should (...) include the option that future research be restricted to the illness being studied. A slight majority (66.2%) would donate their samples for future genetic research. Respondents were more favourable towards having their blood samples exported to other Arab countries (62.0%) compared with countries in Europe (41.8%, p<0.001) and to the USA (37.2%, p<0.001). Conclusions This study shows that many individuals do not favour the donation of a blood sample for future research. Of those who do approve of such future research, many favour a consent model that includes an option restricting the future research to the illness being studied. Also, many Egyptians were hesitant to have their blood samples donated for genetic research or exported out of the Arab region to the USA and European countries. Further qualitative research should be performed to determine the underlying reasons for many of our results. (shrink)

Liquidity risk arises from the inability to unwind or hedge trading positions at the prevailing market prices. The risk of liquidity is a wide and complex topic as it depends on several factors and causes. While much has been written on the subject, there exists no clear-cut mathematical description of the phenomena and typical market risk modeling methods fail to identify the effect of illiquidity risk. In this paper, we do not propose a definitive one either, but we attempt to (...) derive novel mathematical algorithms for the dynamic modeling of trading volumes during the closeout period from the perspective of multiple-asset portfolio, as well as for financial entities with different subsidiary firms and multiple agents. The robust modeling techniques are based on the application of initial-value-problem differential equations technique for portfolio selection and risk management purposes. This paper provides some crucial parameters for the assessment of the trading volumes of multiple-asset portfolio during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed-form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half-life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. The developed modeling algorithms are appealing in terms of theory and are promising for practical econophysics applications, particularly in developing dynamic and robust portfolio management algorithms in light of the 2007–2009 global financial crunch. In addition, they can be applied to artificial intelligence and machine learning for the policymaking process, reinforcement machine learning techniques for the Internet of Things data analytics, expert systems in finance, FinTech, and within big data ecosystems. (shrink)