We apply Hrushovski-Fraïssé's amalgamation procedure to obtain a theory of fields of prime characteristic of Morley rank 2 equipped with a definable additive subgroup of rank 1.

Let T1 and T2 be two countable strongly minimal theories with the DMP whose common theory is the theory of vector spaces over a fixed finite field. We show that T1 ∪ T2 has a strongly minimal completion.

Summary. From known examples of theories T obtained by Hrushovski-constructions and of infinite Morley rank, properties are extracted, that allow the collapse to a finite rank substructure. The results are used to give a more model-theoretic proof of the existence of the new uncountably categorical groups in [3].

In this paper we construct a non-CM-trivial stable theory in which no infinite field is interpretable. In fact our theory will also be trivial and ω-stable, but of infinite Morley rank. A long term aim would be to find a nonCM-trivial theory which has finite Morley rank (or is even strongly minimal) and does not interpret a field. The construction in this paper is direct, and is a “3-dimensional” version of the free pseudoplane. In a sense we are cheating: the (...) original point of the notion ofCM-triviality was to describe the geometry of a strongly minimal set, or even of a regular type. In our example, non-CM-triviality will come from the behaviour of three orthogonal regular types.A stable theory is said to beCM-trivial if wheneverA⊆Band acl(Ac) ∩ acl(B) = acl(A) inTeq, then Cb(stp(c/A)) ⊆ Cb(stp(c/B)). ( An infinite stable field will not beCM-trivial.) The notion is due to Hrushovski [3], where he gave several equivalent definitions, as well as showing that his new strongly minimal sets constructed “ab ovo” wereCM-trivial. The notion was studied further in [6] where it was shown thatCM-trivial groups of finite Morley rank are nilpotent-by-finite. These results were generalized in various ways to the superstable case in [8]. (shrink)

The paper continues [1]. Let S be a complete theory of ultraflat (e.g. planar) graphs as introduced in [4]. We show a strong form of NOTOP for S: The union of two models M1 and M2, independent over a common elementary submodel M0, is the primary model over M1 ∪ M2 of S. Then by results of [1] Mekler's construction [6] gives for such a theory S of nice ultraflat graphs a superstable 2-step-nilpotent group of exponent $p (>2)$ with NDOP (...) and NOTOP. (shrink)

We prove the elimination of Magidor-Malitz quantifiers for R-modules relative to certain Q 2 α -core sentences and positive primitive formulas. For complete extensions of the elementary theory of R-modules it follows that all Ramsey quantifiers (ℵ 0 -interpretation) are eliminable. By a result of Baldwin and Kueker [1] this implies that there is no R-module having the finite cover property.

In a recent communication an uncountably categorical group has been constructed that has a non-locally-modular geometry and does not allow the interpretation of a field. We consider a system Δ of elementary axioms fulfilled by some special subgroups of the above group. We show that Δ is complete and stable, but not superstable. It is not even a R-group in the sense discussed by Wagner.

For every structure M of finite signature Mekler 781) has constructed a group G such that for every κ the maximal number of n -types over an elementary equivalent model of cardinality κ is the same for M and G . These groups are nilpotent of class 2 and of exponent p , where p is a fixed prime greater than 2. We consider stable structures M only and show that M is CM -trivial if and only if G is (...) CM -trivial. Furthermore, we obtain that the free group F 2 in the variety of 2 -nilpotent groups of exponent p>2 with ω free generators has a CM -trivial ω -stable theory. (shrink)

It is possible to define a combinatorial closure on alternating bilinear maps with few relations similar to that in [2]. For the ℵ 0 - categorical case we show that this closure is part of the algebraic closure.

Let S and T be countable complete theories. We assume that T is superstable without the dimensional order property, and S is interpretable in T in such a way that every model of S is coded in a model of T. We show that S does not have the dimensional order property, and we discuss the question of whether $\operatorname{Depth}(S) \leq \operatorname{Depth}(T)$ . For Mekler's uniform interpretation of arbitrary theories S of finite similarity type into suitable theories T s of (...) groups we show that $\operatorname{Depth}(S) \leq \operatorname{Depth}(T_S) \leq 1 + \operatorname{Depth}(S)$. (shrink)

The elementary theory of a nontrivial free Lie algebra over a commutative integral domain is unstable and has the strict order property.

Let T be a countable, complete, ω-stable, nonmultidimensional theory. By Lascar [7], in T eq there is in every dimension of T a type with Lascar rank ω α for some α. We give sufficient conditions for α to coincide with the level of that dimension in Pillay's [10] RK-hierarchy of dimensions computed in T eq . In particular, this is fulfilled for modules.

Let L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} be the language of group theory with n additional new constant symbols c1,…,cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c_1,\ldots,c_n}$$\end{document}. In L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}$$\end{document} we consider the class K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{K}}}$$\end{document} of all finite groups G of exponent p>2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${p > 2}$$\end{document}, where G′⊆⟨c1G,…,cnG⟩⊆Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G'\subseteq\langle c_1^G,\ldots,c_n^G\rangle \subseteq Z}$$\end{document} and c1G,…,cnG\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c_1^G,\ldots,c_n^G}$$\end{document} are linearly independent. Using amalgamation we show the existence of Fraïssé limits D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} of K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb{K}}}$$\end{document}. D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} is Felgner’s extra special p-group. The elementary theories of the D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}$$\end{document} are supersimple of SU-rank 1. They have the independence property. (shrink)

One of Hume's most well-known works and a masterpiece of philosophy, A Treatise of Human Nature is indubitably worth taking the time to read.

Several attempts have been done to distinguish “positive” information in an arbitrary first order theory, i.e., to find a well behaved class of closed sets among the definable sets. In many cases, a definable set is said to be closed if its conjugates are sufficiently distinct from each other. Each such definition yields a class of theories, namely those where all definable sets are constructible, i.e., boolean combinations of closed sets. Here are some examples, ordered by strength:Weak normality describes a (...) rather small class of theories which are well understood by now (see, for example, [P]). On the other hand, normalization is so weak that all theories, in a suitable context, are normalizable (see [HH]). Thus equational theories form an interesting intermediate class of theories. Little work has been done so far. The original work of Srour [S1, S2, S3] adopts a point of view that is closer to universal algebra than to stability theory. The fundamental definitions and model theoretic properties can be found in [PS], though some easy observations are missing there. Hrushovski's example of a stable non-equational theory, the first and only one so far, is described in the unfortunately unpublished manuscript [HS]. In fact, it is an expansion of the free pseudospace constructed independently by Baudisch and Pillay in [BP] as an example of a strictly 2-ample theory. Strong equationality, defined in [Hr], is also investigated in [HS]. (shrink)

While there are numerous doubts, controversies and lack of consensus on alternative definitions of human death, it is argued that it is more ethical to allow people to choose either cessation of cardio-respiratory function or loss of entire brain function as the definition of death based on their own views. This paper presents the law of organ transplantation in Japan, which allows people to decide whether brain death can be used to determine their death in agreement with their family. Arguably, (...) Japan could become a unique example of individual choice in the definition of death if the law is revised to allow individuals choose definition of death independently of their family. It suggests that such an approach is one of the reasonable policy options a country can adopt for legislation on issues related to the definition of death. (shrink)

Ludwig Wittgenstein (1889-1951) was an extraordinarily original thinker, whose influence on twentieth-century thinking far outside the bounds of philosophy alone. In this engaging Introduction, A.C. Grayling makes Wittgenstein's thought accessible to the general reader by explaining the nature and impact of Wittgenstein's views. He describes both his early and later philosophy, the differences and connections between them, and gives a fresh assessment of Wittgenstein's continuing influence on contemporary thought.

Background: The magnitude of bullying and harassment among psychiatrists is reportedly high, yet no peer-review published studies addressing this issue could be found. Therefore, it was decided to conduct a pilot study to assess the degree of the problem, the types of bullying/harassment and to provide some insights into the situation.Methods and Principal Findings: Following multiple focus group meetings, a yes/no response type questionnaire was developed to assess the degree and type of bullying and harassment experienced by psychiatrists. Over a (...) 3-month period the questionnaire was administered to a random sample of 60 psychiatrists. 57 out of the 60 psychiatrists reported harassment and bullying. Frequencies of the following response variables are presented in descending order: rumours 40% ; defamation 20% ; passing remarks 20% ; false accusations 15% ; threats 13.3% ; verbal abuse 13.3% ; unjustified complaints 13.3% ; promotion blocked 13.3% ; humiliation 13% ; bad reference given 10% ; credentials questioned 8.3% ; physical attacks 5% ; termination 5% ; derogatory remarks 1.7% and 1.7% were subjected to personal work. As a result of being subjected to harassment, 66.7% of the psychiatrists did not take any action, whereas 33.3% confronted the person they believed responsible. Asked whether the bullying and harassment caused distress, 18.3% of the psychiatrists did not report any effect, 30% reported mild distress, 40% moderate distress and severe distress was reported by 11.7%.Conclusions: It was concluded that the magnitude of bullying and harassment among psychiatrists may be quite high, as evidenced by this pilot study. There is a need for extensive systematic studies on this subject and to establish strategies to prevent and address this issue at a national and regulatory level. (shrink)

Is unethical conduct necessarily irrational? Answering this question requires giving an account of practical reason, of practical good, and of the source or point of wrongdoing. By the time most contemporary philosophers have done the first two, they have lost sight of the third, chalking up bad action to rashness, weakness of will, or ignorance. In this book, Candace Vogler does all three, taking as her guides scholars who contemplated why some people perform evil deeds. In doing so, she sets (...) out to at once engage and redirect contemporary debates about ethics, practical reason, and normativity. -/- Staged as a limited defense of a standard view of practical reason (an ancestor of contemporary instrumentalist views), Vogler's essay develops Aquinas's remark about three ways an action might be desirable into an exhaustive system for categorizing reasons for acting. Drawing on Elizabeth Anscombe's pioneering work on intention, Vogler argues that one sort (means/end or calculative reasons for acting) sets the terms for all sound work on practical rationality. -/- She takes up Aquinas's work on evil throughout, arguing that he provides us with a systematic theory of immorality that takes seriously the goods at issue in wrongdoing and the reasons for unethical conduct. Vogler argues that, shorn of its theological context, this theory leaves us with no systematic, uncontroversial way of arguing that wrongdoing is necessarily contrary to reason. (shrink)

The urgency of the research topic is that the theoretical and methodological principles of psychology of managerial activity of the head in the conditions of the information society help to increase the levers of management and guidance. The purpose of management - the receipt of the desired result, which must be obtained after the actions of the management of the head as the main operating force, which is heading for transformations, tries to increase the self-governing principle in the organization. The (...) problem of research is that for effective management it is necessary to develop reliable mechanisms for the identification and development of manager's abilities, to increase the level of professionalism and competence of the head to the highest level, so that the management organism does not disorient. A person who works as a specialist, a professional, a competent person can be qualified to carry out the work of a manager. The hypothesis is put forward that the manager of a high level of professionalism and competence is able to form the psychological foundations of the organization, so that it worked as a single social organism. The task of the research is to analyze the psychological foundations of management activity in the conditions of the information society, which would allow the most optimal management of a particular organization. The methodological foundations of the psychology of management as the basis of effective leadership include methods of cultural development, which are used to solve the problems of organization, the formation of psychological culture, devoid of conflicts, contradictions, disasters. Methodological basis of scientific research of psychological principles of administrative activity as the basis of effective management are methods, such as system, structural, structural-functional, historical, comparative, which allow to achieve a higher level of organization and self-organization at the expense of skilful leadership. Therefore, the manager must use the whole set of methods, techniques, algorithms of actions, techniques, methods of achieving certain results that will lead to the management of a high level. It is concluded that the determinants of the optimization of the managerial psychology of the head is a model aimed at regulating relationships, which would use the resources of the information society, which is based on high information provision for improving the efficiency of management work. (shrink)

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much (...) more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included. (shrink)

This exciting new Handbook offers a comprehensive overview of the contemporary state of the field. The editors' introduction and forty-five essays cover feminist critical engagements with philosophy and adjacent scholarly fields, as well as feminist approaches to current debates and crises across the world. Authors cover topics ranging from the ways in which feminist philosophy attends to other systems of oppression, and the gendered, racialized, and classed assumptions embedded in philosophical concepts, to feminist perspectives on prominent subfields of philosophy. The (...) first section contains chapters that explore feminist philosophical engagement with mainstream and marginalized histories and traditions, while the second section parses feminist philosophy's contributions to with numerous philosophical subfields, for example metaphysics and bioethics. A third section explores what feminist philosophy can illuminate about crucial moral and political issues of identity, gender, the body, autonomy, prisons, among numerous others. The Handbook concludes with the field's engagement with other theories and movements, including trans studies, queer theory, critical race, theory, postcolonial theory, and decolonial theory. The volume provides a rigorous but accessible resource for students and scholars who are interested in feminist philosophy, and how feminist philosophers situate their work in relation to the philosophical mainstream and other disciplines. Above all it aims to showcase the rich diversity of subject matter, approach, and method among feminist philosophers. (shrink)

The Problem of Perception offers two arguments against direct realism--one concerning illusion, and one concerning hallucination--that no current theory of ...