The Cherlin–Zil'ber Conjecture states that all simple groups of finite Morley rank are algebraic. We prove that any minimal counterexample to this conjecture has a unique conjugacy class of Carter subgroups, which are analogous to Cartan subgroups in algebraic groups.

In this paper the following theorem is proved regarding groups of finite Morley rank which are perfect central extensions of quasisimple algebraic groups.Theorem1.Let G be a perfect group of finite Morley rank and let C0be a definable central subgroup of G such that G/C0is a universal linear algebraic group over an algebraically closed field; that is G is a perfect central extension of finite Morley rank of a universal linear algebraic group. Then C0= 1.Contrary to an impression which exists in (...) some circles, the center of the universal extension of a simple algebraic group, as an abstract group, is not finite in general. Thus the finite Morley rank assumption cannot be omitted.Corollary1.Let G be a perfect group of finite Morley rank such that G/Z(G) is a quasisimple algebraic group. Then G is an algebraic group. In particular, Z(G) is finite([4],Section27.5).An understanding of central extensions of quasisimple linear algebraic groups which are groups of finite Morley rank is necessary for the classification oftamesimpleK*-groupsof finite Morley rank, which constitutes an approach to the Cherlin-Zil’ber conjecture. For this reason the theorem above and its corollary were proven in [1] (Theorems 4.1 and 4.2) under the assumption oftameness, which simplifies the argument considerably. The result of the present paper shows that this assumption can be dropped. The main line of argument is parallel to that in [1]; the absence of the tameness assumption will be countered by a model-theoretic result and results fromK-theory. The model-theoretic result places limitations on definability in stable fields, and may possibly be relevant to eliminating certain other uses of tameness. (shrink)

We know quite a lot about the general structure of ω-stable solvable centerless groups of finite Morley rank. Abelian groups of finite Morley rank are also well-understood. By comparison, nonabelian nilpotent groups are a mystery except for the following general results:• An ω1-categorical torsion-free nonabelian nilpotent group is an algebraic group over an algebraically closed field of characteristic 0 [Z3].• A nilpotent group of finite Morley rank is the central product of a definable subgroup of finite exponent and of a (...) definable divisible subgroup [N3].• A divisible nilpotent group of finite Morley rank is the direct product of its torsion part (which is central) and of a torsion-free subgroup [N3].However, we do not understand nilpotent groups of bounded exponent. It seems that the classification of nilpotent (but nonabelian)p-groups of finite Morley rank is impossible. Even the nilpotent groups of Morley rank 2 contain insurmountable difficulties [C], [T]. At first glance, this may seem to be an obstacle to proving the Cherlin-Zil'ber conjecture (“simple groups of finite Morley rank are algebraic groups”). Our purpose in this article is to show that if such a group is a definable subgroup of a nonnilpotent group, then it is possible to obtain a classification within the boundaries of our present knowledge. In this respect, our article may be considered as a relief to those who are trying to classify simple groups of finite Morley rank.Before explicitly stating our result, we need the following definition. (shrink)

§1. Introduction. By and large, definitions of a differentiable structure on a set involve two ingredients, topology and algebra. However, in some cases, partial information on one or both of these is sufficient. A very simple example is that of the field ℝ where algebra alone determines the ordering and hence the topology of the field:In the case of the field ℂ, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the ield but (...) this will be too coarse to give a diferentiable structure.A celebrated example of how partial algebraic and topological data determines a differentiable structure is Hilbert's 5th problem and its solution by Montgomery-Zippin and Gleason.The main result which we discuss here is of a similar flavor: we recover an algebraic and later differentiable structure from a topological data. We begin with a linearly ordered set ⟨M, <⟩, equipped with the order topology, and its cartesian products with the product topologies. We then consider the collection of definable subsets of Mn, n = 1, 2, …, in some first order expansion ℳ of ⟨M, <⟩. (shrink)

We show that is a quasi-minimal torsion-free divisible abelian group. After discussing the axiomatization of the theory of this structure, we present its ω-saturated quasi-minimal model.

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)

Reviewed Works:B. I. Zil'ber, L. Pacholski, J. Wierzejewski, A. J. Wilkie, Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. II.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. III.B. I. Zil'ber, E. Mendelson, Totally Categorical Structures and Combinatorial Geometries.B. I. Zil'ber, The Structure of Models of Uncountably Categorical Theories.

In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem.

The notion of quasi-minimal structures was defined by B. Zil'ber as a natural generalization of minimal structures. Inspired by his work, we study here basic model theoretic properties of quasiminimal structures. Main result is the construction of ω-saturated quasi-minimal models under ω-stability assumption.

CM-triviality of a stable theory is a notion introduced by Hrushovski [1]. The importance of this property is first that it holds of Hrushovski's new non 1-based strongly minimal sets, and second that it is still quite a restrictive property, and forbids the existence of definable fields or simple groups (see [2]). In [5], Frank Wagner posed some questions aboutCM-triviality, asking in particular whether a structure of finite rank, which is “coordinatized” byCM-trivial types of rank 1, is itselfCM-trivial. (Actually Wagner (...) worked in a slightly more general context, adapting the definitions to a certain “local” framework, in which algebraic closure is replaced byP-closure, forPsome family of types. We will, however, remain in the standard context, and will just remark here that it is routine to translate our results into Wagner's framework, as well as to generalise to the superstable theory/regular type context.) In any case we answer Wagner's question positively. Also in an attempt to put forward some concrete conjectures about the possible geometries of strongly minimal sets (or stable theories) we tentatively suggest a hierarchy of geometric properties of forking, the first two levels of which correspond to 1-basedness andCM-triviality respectively. We do not know whether this is a strict hierarchy (or even whether these are the “right” notions), but we conjecture that it is, and moreover that a counterexample to Cherlin's conjecture can be found at level three in the hierarchy. (shrink)

We comment on an early and inspiring remark of an Omskian mathematician concerning the Cherlin—Zilber Conjecture, meeting in passing some well-known properties of algebraic groups whose generalization to arbitrary groups of finite Morley rank seems to be very uncertain. This paper assumes a familiarity with the model theoretic tools involved in the study of the groups of finite Morley rank.

The received view on the development of the correspondence rules in Carnap’s philosophy of science is that at first, Carnap assumed the explicit definability of all theoretical terms in observational terms and later weakened this assumption. In the end, he conjectured that all observational terms can be explicitly defined in in theoretical terms, but not vice versa. I argue that from the very beginning, Carnap implicitly held this last view, albeit at times in contradiction to his professed position. To establish (...) this point I argue that, first, Carnap’s ‘Über die Aufgabe der Physik’ is a contribution to the philosophy of science of logical empiricism, contrary to Thomas Mormann and in agreement with Herbert Feigl. Second, Michael Friedman misunderstands the ‘Aufgabe’ with his claim that it describes a method for arriving at explicit definitions for theoretical terms. Another received view on Carnap’s philosophy of science is that it assumed a formalization of physical theories that was too detached from actual physics and thus justly disavowed in favor of the semantic view as, for example, developed by van Fraassen. But the ‘Aufgabe’ and related works including the Aufbau show that from the very beginning to his last works, Carnap suggested formalizing physical theories as restrictions in mathematical spaces, as in the state-space conception of scientific theories favored by van Fraassen. (shrink)

John Dewey’s Metaphysical Theory provides an overview and technical exposition of Dewey’s mature ontological theory. In particular, “nature,” “experience,” and their relationship, are given extended treatment through a close reading of primary texts. Following Dewey’s metaphysical postulates and conclusions, the book suggests how experience may reveal the fundamental traits of nature. In addition, the book reveals how Dewey understood the ways in which all phenomena may relate within an inclusive economy of existence, what it means to have an “identity,” what (...) constitutes “selfhood” or personality, and how metaphysics relates to the ideals of democracy and social ethics. (shrink)

We prove the hereditary undecidability of the L t theories of: (1) torsion-free Hausdorff topological abelian groups; (2) locally pure Hausdorff topological abelian groups.

The introduction of contraceptive technologies hasresulted in the separation of sex and procreation. Theintroduction of new reproductive technologies (mainlyIVF and embryo transfer) has led not only to theseparation of procreation and sex, but also to there-definition of the terms mother and family.For the purpose of this essay, I will distinguishbetween:1. the genetic mother – the donor of the egg;2. the gestational mother – she who bears and gives birth to the baby;3. the social mother – the woman who raises the (...) child.This essay will deal only with the form of gestationalsurrogacy in which the genetic parents intend to bethe social parents, and the surrogate mother has nogenetic relationship to the child she bears anddelivers. I will raise questions regarding medicalethical aspects of surrogacy and the obligation(s) ofthe physician(s) to the parties involved. I will arguethat the gestational surrogate is a womb to rent,that there is great similarity between gestationalcommercial surrogacy and organ transplant marketing.Furthermore, despite claims to freedom of choice andfree marketing, I will claim that gestationalsurrogacy is a form of prostitution and slavery,exploitation of the poor and needy by those who arebetter off. The right to be a parent, although notconstitutional, is intuitive and deeply rooted.However, the issue remains whether this rightoverrules all other rights, and at what price to theparties involved. I will finally raise the followingprovocative question to society: In the interim periodbetween today''s limited technology and tomorrow''sextra-corporeal gestation technology (ectogenesis),should utilizing females in PVS (persistent vehetativestate) for gestational surrogacy be sociallyacceptable/permissible – provided they have leftpermission in writing? (shrink)

The problem of the existence of a universal structure omitting a finite set of forbidden substructures is reducible to the corresponding problem in the category of graphs with a vertex coloring by two colors. It is not known whether this problem reduces further to the category of ordinary graphs. It is also not known whether these problems are decidable.

THEOREM. The Jacobson radical of an ℵ 0 -categorical associative ring is nilpotent.

We analyze the two cardinal properties of definable sets in homogeneous graphs.

Prior research flags the inherent incompatibilities between for-profit and nonprofit partners and cautions that clashing value creation logics and conflicting identities can stall social innovation in cross sector partnerships. Process narratives of successful versus unsuccessful cross sector partnerships paint a more optimistic picture, whereby the frequency, intensity, breadth, and depth of interactions may afford frame alignment despite partners' divergent value creation approaches. However, little is known about how cross sector partners come to recognize and reconcile their divergent value creation frames (...) in order to co-construct social value. Using longitudinal narratives of four dyads, we show that partners initially contrast their sector-embedded diagnostic frames and then work together to deliberately develop partnership-specific prognostic frames. We extend the literature on framing by developing a four-stage grounded model of frame negotiation, elasticity, plasticity, and fusion which unpacks the relational process of value creation in cross sector partnerships. Our qualitative analyses further show how partners orchestrate multilevel coordination that helps scaffold and calibrate this relational process of frame fusion. (shrink)

The essay that follows discusses an ordered series of situated environmental “fields” that comprise John Dewey’s “emergent naturalism.” These fields include nature, experience, mind, subconscious, consciousness, and cognitive thought. I propose an order to these fields, and provide an overview of the ways in which fields that are larger in scope stand as the conditions for those that are more limited. I also suggest ways in which cognitive thought further emerges through the process of inquiry. This emergent scheme culminates in (...) a type of inquiry where an agent actively creates conflict in order to enrich experience. (shrink)

Irony, one of the most basic, pervasive, and variegated of rhetorical tropes, is as fundamental to musical thought as it is to poetry, prose, and spoken language. In this wide-ranging study of musical irony, Michael Cherlin draws upon the rich history of irony as developed by rhetoricians, philosophers, literary scholars, poets, and novelists. With occasional reflections on film music and other contemporary works, the principal focus of the book is classical music, both instrumental and vocal, ranging from Mozart to Mahler. (...) The result is a surprising array of approaches toward the making and interpretation of irony in music. Including nearly ninety musical examples, the book is clearly structured and engagingly written. This interdisciplinary volume will appeal to those interested in the relationship between music and literature as well as to scholars of musical composition, technique, and style. (shrink)

Managing aggression in mental health hospitals is an important and challenging task for clinical nursing staff. A majority of studies focus on the perspective of clinicians, and research mainly depicts aggression by referring to patient-related factors. This qualitative study investigates how aggression is communicated in forensic mental health nursing records. The aim of the study was to gain insight into the discursive practices used by forensic mental health nursing staff when they record observed aggressive incidents. Textual accounts were extracted from (...) the Staff Observation Aggression Scale-Revised (SOAS-R), and Fairclough’s Critical Discourse Analysis was used to identify short narrative entries depicting patients and staffs in typical ways. The narratives contained descriptions of complex interactions between patient and staff that were linked to specific circumstances surrounding the patient. These antecedents, combined with the aggression incident itself, created stereotyping representations of forensic psychiatric patients as deviant, unpredictable and dangerous. Patient and staff identities were continually (re)produced by an automatic response from the staff that was solely focused on the patient’s behavior. Such response might impede implementation of new strategies for managing aggression. (shrink)

We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group". These results are quickly finding extensive applications within the classification project.

We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Z p n or the Witt ring W 2 (F 4 ) (which is the characteristic four analogue of the Galois field with four elements).

We study definable irreducible actions of SL₂(K) on an abelian group of Morley rank ≤ 3rk(K) and prove they are rational representations of the group.

The 1925 publication of Experience and Nature marks a new period in John Dewey's thought: he had become interested in developing a naturalistic metaphysics. Despite his new metaphysical orientation, Dewey's mature philosophy is compatible with and builds upon works that fall within his Middle Period, from 1903–1924.1 While this is usually accepted as true, my more substantial claim is that we cannot get a clear picture of Dewey's metaphysics apart from what came before. More than simply showing that Dewey's characterization (...) of specific topics, such as "logic," or specific terms, such as "belief," are compatible with his later discussions, this article will demonstrate that the broader dynamics, themes, and... (shrink)