We deal with two forms of the "uniqueness cases" in the classification of large simple K*-groups of finite Morley rank of odd type, where large means the 2-rank m2 is at least three. This substantially extends results known for even larger groups having Prüfer 2-rank at least three, so as to cover the two groups PSp 4 and G 2. With an eye towards more distant developments, we carry out this analysis for L*-groups, a context which is substantially broader than (...) the K* setting. (shrink)

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)

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)

A personal voyage of discovery drawing on musicology, literary theory, Jewish studies, and philosophical phenomenology.

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.

This is a welcome reprint of a book that continues to grow in importance.

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)

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

In John Dewey’s logical theory, qualities or qualitative relations account for the capacity to distinguish and associate the objects of reflective thought; they are antecedent to reflective analysis and necessary for coherent processes of inquiry. In Dewey’s writings that are specifically “metaphysical” in orientation, he is much more vague about the function of qualities, but does call them “generic traits of existence.” As such, they appear to be central to his mature ontological theory. In order to more fully understand the (...) metaphysical import of qualitative relations, I first examine the details of Dewey’s logical theory, and then generalize those details in accordance with Dewey’s larger theory of nature. The end result is a novel interpretation of Dewey’s metaphysics. (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.

Borovik proposed an axiomatic treatment of Morley rank in groups, later modified by Poizat, who showed that in the context of groups the resulting notion of rank provides a characterization of groups of finite Morley rank [2]. (This result makes use of ideas of Lascar, which it encapsulates in a neat way.) These axioms form the basis of the algebraic treatment of groups of finite Morley rank undertaken in [1].There are, however, ranked structures, i.e., structures on which a Borovik-Poizat rank (...) function is defined, which are not ℵ0-stable [1, p. 376]. In [2, p. 9] Poizat raised the issue of the relationship between this notion of rank and stability theory in the following terms: “… ungroupede Borovik est une structure stable, alors qu'un univers rangé n'a aucune raison de l'être …” (emphasis added). Nonetheless, we will prove the following:Theorem 1.1.A ranked structure is superstable.An example of a non-ℵ0-stable structure with Borovik-Poizat rank 2 is given in [1, p. 376]. Furthermore, it appears that this example can be modified in a straightforward way to give ℵ0-stable structures of Borovik-Poizat rank 2 in which the Morley rank is any countable ordinal (which would refute a claim of [1, p. 373, proof of C.4]). We have not checked the details. This does not leave much room for strenghthenings of our theorem. On the other hand, the proof of Theorem 1.1 does give a finite bound for the heights of certain trees of definable sets related to unsuperstability, as we will see in Section 5. (shrink)

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).

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.

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)

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)

Emergentism is an important and yet underexplored component of John Dewey’s metaphysical program, and concerns the ways in which existences relate, operate, and grow in coordination with a more inclusive environment. Through an emergent account, Dewey addresses continuities among the generic traits of nature, inanimate substance, biological life, and experiential “fields” such as mind and consciousness. The notion of a field is especially important for depicting the ways in which existences serially interact in accordance with some particular purpose or set (...) of functions. Apart from an emergent scheme that contextualizes the interactive contexts of experience, phenomena such as “mind” and “consciousness” remain enigmatic occurrences. Moreover, cognition, and with it instances of “knowing,” remain susceptible to merely “subjective” characterizations that reinforce a misleading dualism between mind and nature. In addition to its role in addressing naturalistic continuities, Dewey’s emergentism suggests a non-reductive philosophical methodology that directly challenges contemporary varieties of realism and materialism. (shrink)

THEOREM. The Jacobson radical of an $\aleph_0$-categorical associative ring is nilpotent.

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