We provide a general theorem implying that for a (strongly) dependent theory T the theory of sufficiently well-behaved pairs of models of T is again (strongly) dependent. We apply the theorem to the case of lovely pairs of thorn-rank one theories as well as to a setting of dense pairs of first-order topological theories.

We develop a new notion of independence (þ-independence, read "thorn"-independence) that arises from a family of ranks suggested by Scanlon (þ-ranks). We prove that in a large class of theories (including simple theories and o-minimal theories) this notion has many of the properties needed for an adequate geometric structure. We prove that þ-independence agrees with the usual independence notions in stable, supersimple and o-minimal theories. Furthermore, we give some evidence that the equivalence between forking and þ-forking in simple theories might (...) be closely related to one of the main open conjectures in simplicity theory, the stable forking conjecture. In particular, we prove that in any simple theory where the stable forking conjecture holds. þ-independence and forking independence agree. (shrink)

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all (...) ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

We study dp-minimal and strongly dependent theories and investigate connections between these notions and weight.

We develop the theory of domination by stable types and stable weight in an arbitrary theory.

Let M be an arbitrary structure. Then we say that an M -formula φ defines a stable set inM if every formula φ ∧ α is stable. We prove: If G is an M -definable group and every definable stable subset of G has U -rank at most n , then G has a maximal connected stable normal subgroup H such that G /H is purely unstable. The assumptions hold for example if M is interpretable in an o-minimal structure.More generally, (...) an M -definable set X is weakly stable if the M -induced structure on X is stable. We observe that, by results of Shelah, every weakly stable set in theories with NIP is stable. (shrink)

We examine several conditions, either the existence of a rank or a particular property of þ-forking that suggest the existence of a well-behaved independence relation, and determine the consequences of each of these conditions towards the rosiness of the theory. In particular we show that the existence of an ordinal valued equivalence relation rank is a (necessary and) sufficient condition for rosiness.

This paper is devoted to understand groups definable in Presburger Arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded abelian group definable in a model of (Z, +, <) Presburger Arithmetic is definably isomorphic to (Z, +)^n mod out by a lattice.

We study the behaviour of stable types in rosy theories. The main technical result is that a non-þ-forking extension of an unstable type is unstable. We apply this to show that a rosy group with a þ-generic stable type is stable. In the context of super-rosy theories of finite rank we conclude that non-trivial stable types of U þ -rank 1 must arise from definable stable sets.

In this paper, we prove the following:Theorem. Let M be a rosy dependent theory and letp,pbe non-þ-forking extensions ofp∈Switha0a1; assume thatp∪pis consistent and thata0,a1start a þ-independent indiscernible sequence. Thenp∪pis a non-þ-forking extension ofp.We also provide an example to show that the result is not true without assuming NIP.

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.

Ross, Alf Loar, Brian, Editor.Directives and Norms. New York: Humanities Press, [1967]. ix, 188 pp. Reprint available April 2009 by The Lawbook Exchange, Ltd. ISBN-13: 978-1-58477-961-2. ISBN-10: 1-58477-961-6. Cloth with dust jacket. $65.00 * Reprint of the first American edition. One of the most interesting jurists of the post-World War II era, Ross [1899-1979] was a legal and moral philosopher, scholar of international law and the leading representative of Scandinavian Legal Realism. This book and On Law and Justice (1958) are (...) his principal works. In Directives and Norms Ross asks whether imperatives (or, to use his term, 'directives') are subject to logic in the same way as indicatives. He shows the difference between indicative and directive discourse and explains the concepts 'directive' and 'norm' as they function in the social sciences, especially in the study of law. A contemporary essay in the Modern Law Review (32:544), though critical of this work, was still impressed by its "clear and convincing account" of these processes. (shrink)

Reprint of the first American edition. One of the most interesting jurists of the post-World War II era, Ross [1899-1979] was a legal and moral philosopher, scholar of international law and the leading representative of Scandinavian Legal Realism. This book and On Law and Justice (1958) are his principal works. In Directives and Norms Ross asks whether imperatives (or, to use his term, 'directives') are subject to logic in the same way as indicatives. He shows the difference between indicative and (...) directive discourse and explains the concepts 'directive' and 'norm' as they function in the social sciences, especially in the study of law. A contemporary essay in the Modern Law Review (32:544), though critical of this work, was still impressed by its "clear and convincing account" of these processes. (shrink)

A theme of abiding interest in religious studies is the sharp contrast between cultures with a monotheistic paternal deity and cultures with pluralistic maternal deities. These two principles for organizing religious life are vast; attempts to understand their implications lead to an overwhelmingly diverse set of facts and their meanings. In Freud's India, Alf Hiltebeitel takes up this enormously engaging question, focusing on the thinking of two spokespeople for the inner life of their culture-- Sigmund Freud and Girindrasekhar Bose. Alf (...) Hiltebeitel considers the attempts of these two men to communicate with and understand each other and these issues, in the heated context of emotionally divisive allegiances. The book is elegant in its nuanced attention to these two thinkers, and its tightly controlled exploration of what their interactions indicate about their contributions and limitations as representatives of the psychology and religion of their respective cultures. Anxieties about mothers separate Eastern from Western imaginations. They separate Freud from Bose, and they separate Hindu foundational texts from the Hebrew foundational texts. (shrink)

Ross, Alf. On Law and Justice. Berkeley: University of California Press, 1959. xi, 383 pp. Reprint available December 2004 by the Lawbook Exchange, Ltd.

The existing literature treats of several investigations with a certain bearing on the question which is roughly indicated by the title “Imperatives and Logic.” Some of those investigations, however, are entirely outside the scope of the present work.Mally sets himself the task of developing a “Logik des Willens” constituting a parallel to the usual logic, the “Logik des Denkens". In order to emphasize its independence, the author also calls this “Logik des Willens” “Deontik”, and he conceives it as being based (...) on the “Wesensgesetze” of will in the same way as the usual logic is conceived as being based on the “Wesensgesetze” of thought. The author develops a formalistic deductive system on the basis of 5 axioms of demands, including the axiom that there is at least one fact which is unconditionally demanded, and through a lengthy series of theorems he arrives at the sentence that what is unconditionally demanded is identical with what is actually the case: “was sein soll, ist Tatsache”. Similarly, the author develops a system of axioms for “right” volition, including the axiom that right volition is non-contradictory. (shrink)

Que cherchent les écrivains qui, au risque de passer sous les radars médiatiques, n'empruntent pas l'autoroute du récit linéaire et du reportage romancé? La voie étroite de la poésie débouche sur des formes minoritaires et sur des consistances bizarres de prose. Comme s'il fallait d'urgence ranimer, redessiner les mots en troublant leur usage. Mais dans quel but, au juste? De temps à autre, on m'invite à exposer des idées. Mon choix du sujet est toujours intéressé. Il concerne ce que je (...) pratique : la poésie et la prose narrative surtout, un peu le montage et le dessin. Il s'agit de parler en s'adressant à des gens en particulier. La dispute n'est jamais loin. Le ton n'est pas toujours sérieux. Limité par le temps, je procède quelquefois par simples assertions, qui se lisent alors comme les têtes de chapitres manquants. Esquisses d'une réflexion que d'autres prolongeraient, ces brefs discours sont ensuite laissés en l'état. Ils portent, donc, sur des inventions marginales : poèmes prosaïques, visuels ou animés, récits digressifs ou hétérogènes, figures de monstres, films dansants, fantômes tracés. Ils suggèrent une certaine politique des formes. Ils plaident pour une imagination technique assez négligée — ou mal vue — en littérature. (shrink)