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.

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.

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.

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 classify countable metrically homogeneous graphs of diameter 3.

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.

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

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).

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 classify countable metrically homogeneous graphs of diameter 3.

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)

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)

Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.

In Complicity and Moral Accountability, Gregory Mellema presents a philosophical approach to the moral issues involved in complicity. Starting with a taxonomy of Thomas Aquinas, according to whom there are nine ways for one to become complicit in the wrongdoing of another, Mellema analyzes each kind of complicity and examines the moral status of someone complicit in each of these ways. Mellema's central argument is that one must perform a contributing action to qualify as an accomplice, and that it (...) is always morally blameworthy to perform such an action. Additionally, he argues that an accomplice frequently bears moral responsibility for the outcome of the other's wrongdoing, but he distinguishes this case from cases in which the accomplice is tainted by the wrongdoing of the principal actor. He further distinguishes between enabling, facilitating, and condoning harm, and introduces the concept of indirect complicity. Mellema tackles issues that are clearly important to any case of collective and shared responsibility, yet rarely discussed in depth, always presenting his arguments clearly, concisely, and engagingly. His account of the nonmoral as well as moral qualities of complicity in wrongdoing--especially of the many and varied ways in which principles and accomplices can interact--is highly illuminating. Liberally sprinkled with helpful and nuanced examples, Complicity and Moral Accountability vividly illustrates the many ways in which one may be complicit in wrongdoing. "In Complicity and Moral Accountability, Gregory Mellema has made an immensely important contribution to the discussion of group morality and collective responsibility both within and far beyond professional academic philosophy. His clearly written book will be essential reading." --Fergus Kerr, Honorary Fellow, University of Edinburgh. (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)

Composed of a substantial introduction, twelve original essays produced for this volume, and a new English translation of a personal, intriguing, and little ...

This clear, learner-friendly text helps today's students bridge the gap between everyday culture and critical thinking. The text covers all the basics of critical thinking, beginning where students are, not where we think they should be. Its comprehensiveness allows instructors to tailor the material to their individual teaching styles, resulting in an exceptionally versatile text.

A re-issue of Gregory Bateson's classic work. It summarizes Bateson's thinking on the subject of the patterns that connect living beings to each other and to their environment.

After a period of relative exhaustion, French phenomenology has experienced a powerful revival in the last ten years, with the emer-gence of a “cosmological” paradigm in phenomenology. While this situation is obviously to be welcomed, it also presents contemporary phenomenologists with the challenge of acquiring a compass that will enable them to find their bearings in this rapidly reconfiguring philosophical landscape, and according to principles that still partly elude those who are committed to them. In so doing, the aim of (...) this study is twofold: firstly, to put forward a series of hypotheses as to the way in which it is being structured - and thus to elaborate a typology of contemporary French phenomenologies; and secondly, to attempt to determine the stakes and also the presuppositions of this new philosophical “deal” which, perhaps, remains transitory and, as such, rich in a future that, for the time being, it is only possible to presage. (shrink)

Now in its twentieth year of publication, this rich collection, popular among teachers and students alike, provides an in-depth look at major cases that have shaped the field of medical ethics. The book presents each famous (or infamous) case using extensive historical and contextual background, and then proceeds to illuminate it by careful discussion of pertinent philosophical theories and legal and ethical issues.