An amalgamation base p in a simple theory is stably definable if its canonical base is interdefinable with the set of canonical parameters for the ϕ-definitions of p as ϕ ranges through all stable formulae. A necessary condition for stably definability is given and used to produce an example of a supersimple theory with stable forking having types that are not stably definable. This answers negatively a question posed in [8]. A criterion for and example of a stably (...) definable amalgamation base whose restriction to the canonical base is not axiomatised by stable formulae are also given. The examples involve generic relations over non CM-trivial stable theories. (shrink)

We show that a formula φ(x, y) is stable if and only if φ is the pairing map on the unit ball of E x E * , where E is a reflexive Banach space. The result remains true if the formula φ is replaced by a set of formulas $p(\bar{x},\bar{y})$.

We define a hierarchy on the regular types of an ω-stable nonmultidimensional theory, using generalised notions of algebraic and strongly minimal formulae. As an application we show that any resplendent model of an ω-stable finite-dimensional theory is saturated.

Stable logics are modal logics characterized by a class of frames closed under relation preserving images. These logics admit all filtrations. Since many basic modal systems such as K4 and S4 are not stable, we introduce the more general concept of an M-stable logic, where M is an arbitrary normal modal logic that admits some filtration. Of course, M can be chosen to be K4 or S4. We give several characterizations of M-stable logics. We prove that (...) there are continuum many S4-stable logics and continuum many K4-stable logics between K4 and S4. We axiomatize K4-stable and S4-stable logics by means of stable formulas and discuss the connection between S4-stable logics and stable superintuitionistic logics. We conclude the article with many examples (and nonexamples) of stable, K4-stable, and S4-stable logics and provide their axiomatization in terms of stable rules and formulas. (shrink)

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)

This article describes the relation between the existence of regional parties in Romania vs. stable democracies like Belgium and Germany and the degree of regional issue dimensions reflected by partiesí electoral support. It also reflects the impact of regional dimension on voting behavior. The research is based on the nationalization concept introduced by Mark P. Jones and Scott Mainwaring, well operationalized here by Gini Index based vote share of parties in subunits applied on one or more countries. From here, (...) the study wants to promote a new formula which permits the evaluation of regional dimension from all issue dimensions of a country and counting the score like a reflection of differences between parties (regional, national), the differences between voters expectations on regional issues, the competition pattern, the increase or decrease of the national issue dimensions by changing inside the given party system. (shrink)

Safe first-order formulas generalize the concept of a safe rule, which plays an important role in the design of answer set solvers. We show that any safe sentence is equivalent, in a certain sense, to the result of its grounding—to the variable-free sentence obtained from it by replacing all quantifiers with multiple conjunctions and disjunctions. It follows that a safe sentence and the result of its grounding have the same stable models, and that stable models of a safe (...) sentence can be characterized by a formula of a simple syntactic form. (shrink)

The new result of this paper is that for θ-stable we have S1[θ] = D[θ, L, ∞]. S1 is Hrushovski's rank. This is an improvement of a result of Kim and Pillay, who for simple theories under the assumption that either of the ranks be finite obtained the same identity. Only the first equality is new, the second equality is a result of Shelah from the seventies. We derive it by studying localizations of several rank functions, we get the (...) followingMain Theorem. Suppose that μ is regular satisfying μ ≥ |T|+, p is a finite type, and Δ is a set of formulas closed under Boolean operations. If either R[p, Δ, μ+] < ∞ or p is Δ-stable and μ satisfies “for every sequence {μi : i < |Δ| + ℵ0} of cardinals μi < μ we have that equation image holds”, then S[p, Δ, μ+] = D[p, Δ, μ+] = R[p, Δ, μ+].The S rank above is a localized version of Hrushovski's S1 rank. This rank, as well as our systematic use of local stability, allows us to get a more conceptual proof of the equality of D and R, which is an old result of Shelah. A particular case of the theorem offers a new sufficient condition for the equality of S1 and D[·, L, ∞]. We also manage, due to a more general approach, to avoid some combinatorial difficulties present in Shelah's original exposition. (shrink)

We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes and Rosenthal [12]. In order to do this,•We study and compare three notions of convergence of types in a stable theory: logic convergence, i.e., formula by formula, metric convergence (both already well studied) and convergence of canonical bases. In particular, we characterise א0-categorical stable theories in which the last two agree.•We characterise sequences that admit almost indiscernible sub-sequences.•We apply these tools (...) to the theory of atomless random variables (ARV). We characterise types and notions of convergence of types as conditional distributions and weak/strong convergence thereof, and obtain, among other things, the Main Theorem of Berkes and Rosenthal. (shrink)

The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra $\mathcal {B}$ to each formula. We show some basic results regarding the effect of the properties of $\mathcal {B}$ on the behavior of such types, and show they are particularity well behaved in the case of NIP theories. In particular, we generalize the third author’s result about counting types, as well as the notion of a smooth (...) type and extending a type to a smooth one. We then show that Keisler measures are tied to certain Boolean types and show that some of the results can thus be transferred to measures—in particular, giving an alternative proof of the fact that every measure in a dependent theory can be extended to a smooth one. We also study the stable case. We consider this paper as an invitation for more research into the topic of Boolean types. (shrink)

Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable (...) and (bounded, 1-based or of finite rank) with $I(T, \aleph_0) , then we prove that every good p ∈ S(Q) is τ-stable for any countable Q. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories. (shrink)

We study classes of modules closed under direct sums, [Formula: see text]-submodules and [Formula: see text]-epimorphic images where [Formula: see text] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [Formula: see text]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [Formula: see text]-torsion pure injective modules satisfy this criterion. The argument presented is a model theoretic one. (...) We use in an essential way stable independence relations which generalize Shelah’s non-forking to abstract elementary classes. We show that the classical model theoretic notion of superstability is equivalent to the algebraic notion of a noetherian category for these classes. We use this equivalence to characterize noetherian rings, pure semisimple rings, perfect rings and finite products of finite rings and artinian valuation rings via superstability. (shrink)

We generalize the Unstable Formula Theorem characterization of stable theories from Shelah [11], that a theory T is stable just in case any infinite indiscernible sequence in a model of T is an indiscernible set. We use a generalized form of indiscernibles from [11], in our notation, a sequence of parameters from an L-structure M, , indexed by an L′-structure I is L′-generalized indiscernible inM if qftpL′=qftpL′ implies tpL=tpL for all same-length, finite ¯,j from I. Let Tg (...) be the theory of linearly ordered graphs in the language with signature Lg={<,R}. Let Kg be the class of all finite models of Tg. We show that a theory T has NIP if and only if any Lg-generalized indiscernible in a model of T indexed by an Lg-structure with age equal to Kg is an indiscernible sequence. (shrink)

We introduce tame abstract elementary classes as a generalization of all cases of abstract elementary classes that are known to permit development of stability-like theory. In this paper, we explore stability results in this new context. We assume that [Formula: see text] is a tame abstract elementary class satisfying the amalgamation property with no maximal model. The main results include:. Theorem 0.1. Suppose that [Formula: see text] is not only tame, but [Formula: see text]-tame. If [Formula: (...) see text] and [Formula: see text] is Galois stable in μ, then [Formula: see text], where [Formula: see text] is a relative of κ from first order logic. [Formula: see text] is the Hanf number of the class [Formula: see text]. It is known that [Formula: see text]. The theorem generalizes a result from [17]. It is used to prove both the existence of Morley sequences for non-splitting and the following initial step towards a stability spectrum theorem for tame classes:. Theorem 0.2. If [Formula: see text] is Galois-stable in some [Formula: see text], then [Formula: see text] is stable in every κ with κμ=κ. For example, under GCH we have that [Formula: see text] Galois-stable in μ implies that [Formula: see text] is Galois-stable in μ+n for all n < ω. (shrink)

We investigate some common points between stable structures and weakly small structures and define a structureMto befineif the Cantor-Bendixson rank of the topological space${S_\varphi }\left} \right)$is an ordinal for every finite subsetAofMand every formula$\varphi \left$wherexis of arity 1. By definition, a theory isfineif all its models are so. Stable theories and small theories are fine, and weakly minimal structures are fine. For any finite subsetAof a fine groupG, the traces on the algebraic closure$acl\left$ofAof definable subgroups ofGover$acl\left$which are (...) boolean combinations of instances of an arbitrary fixed formula can decrease only finitely many times. An infinite field with a fine theory has no additive nor multiplicative proper definable subgroups of finite index, nor Artin-Schreier extensions. (shrink)

Abstract.This paper is the second in a series of three culminating in an ordinal analysis of Π12-comprehension. Its objective is to present an ordinal analysis for the subsystem of second order arithmetic with Δ12-comprehension, bar induction and Π12-comprehension for formulae without set parameters. Couched in terms of Kripke-Platek set theory, KP, the latter system corresponds to KPi augmented by the assertion that there exists a stable ordinal, where KPi is KP with an additional axiom stating that every set is (...) contained in an admissible set. (shrink)

In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a first-order formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean- ing of counting and choice by reducing these constructs to first-order formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. (...) We compare the new language with the concept of a disjunc- tive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a frag- ment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen. (shrink)

Once, G. E. Moore scorned the “common point of view which takes the world of experience as ultimately real.” The argument Moore followed to this sceptical conclusion in his fledgling 1897 fellowship dissertation was a legacy from Kant's Antinomies. By 1899 Moore had renounced idealist conclusions; he set out both to disengage from Kantian arguments and to reconcile with “the world of experience.” Moore's work for a stable realist basis for knowledge to fulfil both aims occupied his most famous (...) argument, in his 1939 lecture “Proof of an External World.” Moore himself is sometimes supposed to have thought the argument of this masterwork unsatisfactory where it treats a traditional sceptical puzzle posed by dreaming. Critics, including Wittgenstein, have portrayed Moore's best reply to philosophical scepticism as dogmatic mere assertion, unresponsive or as ineffectual as sheer handwaving. However, these critics rate Moore's success against scepticism based on interpretations of “Proof of an External World” that neglect its part in Moore's campaign against Kant. Consequently, some potentially pivotal questions — which in this study I merely broach — remain wide open; for example, why in presenting his famous 1939 proof did Moore state that its purpose was to refute what “Kant declares to be his opinion, that there is only one possible proof of the existence of things outside of us”? And why did Moore explicitly reject the formula for posing philosophical scepticism in which Kant famously proclaimed this problem “a scandal to philosophy”? (shrink)

We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness, and are stable in some cardinal. Assuming the singular cardinal hypothesis, we prove a full characterization of the stability cardinals, and connect the stability spectrum with the behavior of saturated models.We deduce that if a class is stable on a tail of cardinals, then it has no long splitting chains. This indicates that there is a clear notion of superstability in this framework.We also (...) present an application to homogeneous model theory: for [Formula: see text] a homogeneous diagram in a first-order theory [Formula: see text], if [Formula: see text] is both stable in [Formula: see text] and categorical in [Formula: see text] then [Formula: see text] is stable in all [Formula: see text]. (shrink)

In this paper, we study the introduction of modal past temporal operators in Temporal Equilibrium Logic, an hybrid formalism that mixes linear-time modalities and logic programs interpreted under stable models and their characterisation in terms of Equilibrium Logic. We show that Kamp’s translation can also be used to translate the new extension of TEL with past operators into Quantified Equilibrium Logic. Additionally, we provide a method for removing past operators that consists in replacing past-time subformulas by fresh auxiliary atoms, (...) obtaining an equivalent formula, modulo the original alphabet. (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)

The variety of Heyting algebras has two well-behaved locally finite reducts, the variety of bounded distributive lattices and the variety of implicative semilattices. The variety of bounded distributive lattices is generated by the →-free reducts of Heyting algebras, while the variety of implicative semilattices is generated by the ∨-free reducts. Each of these reducts gives rise to canonical formulas that generalize Jankov formulas and provide an axiomatization of all superintuitionistic logics. The ∨-free reducts of Heyting algebras give rise to the (...) -canonical formulas that we studied in an earlier work. Here we introduce the -canonical formulas, which are obtained from the study of the →-free reducts of Heyting algebras. We prove that every si-logic is axiomatizable by -canonical formulas. We also discuss the similarities and differences between these two kinds of canonical formulas. One of the main ingredients of these formulas is a designated subset D of pairs of elements of a finite subdirectly irreducible Heyting algebra A. When D=A2, we show that the -canonical formula of A is equivalent to the Jankov formula of A. On the other hand, when D=∅, the -canonical formulas produce a new class of si-logics we term stable si-logics. We prove that there are continuum many stable si-logics and that all stable si-logics have the finite model property. We also compare stable si-logics to splitting and subframe si-logics. (shrink)

Le but de cette encyclopédie en deux volumes, rédigée à l’instigation du président Hoover, était d’exposer tous les aspects de la vie sociale américaine, dans le dessein bien arrêté de saisir les rapports existant entre les différentes sphères sociales et de déterminer les transformations qui se produisent au sein de la société. Ces transformations devaient non seulement être constatées, mais on voulait encore essayer de trouver leur tendance générale, leur „trend“, c’est-à-dire la loi qui les détermine. Dans une critique des (...) résultats et des méthodes de cette „expression collective de la recherche sociale aux États-Unis“, M. G. s’efforce de montrer qu’en dépit de l’ampleur considérable de l’ouvrage, qui est également, en quelque sorte, une encyclopédie de la société américaine, le but scientifique visé n’a pas été atteint, et qu’il ne pouvait pas l’être. En effet, la théorie d’Ogburn, qui est à la base de l’ouvrage, et d’après laquelle les crises sont dues à des disproportions dans la vitesse de développement des différentes régions sociales, est insuffisante. Elle présuppose un ordre social relativement stable, dans lequel les dérangements peuvent être considérés comme de simples oscillations autour d’un noyau sain en lui-même. Comme le phénomène fondamental, la crise économique, n’est pas traité, on renonce à reconnaître méthodiquement que tous les processus sociaux sont incontestablement influencés par les faits économiques. Une autre objection importante, illustrée par M. G. au moyen d’une série d’exemples, concerne la notion du „trend“, empruntée à l’étude de la conjoncture. Le „trend“ ne peut pas avoir une loi sociale adéquate, parce qu’il tend à transformer tous les rapports sociaux qualitatifs en rapports mathématico-statistiques de valeurs. Le système actuel de la société, avec ses multiples ramifications, ne pourra toutefois jamais être saisi à i’aide de méthodes uniquement quantitatives ; il exige au contraire, dans son ensemble, une interprétation dynamique de la société. Comme le „Report“ y a renoncé, son intention théorique devait nécessairement échouer. Plus encore : les propositions pratiques qu’il fait pour l’élimination des défauts de la société américaine n’arrivent pas à la racine du mal.The joint report written at the request of president Hoover undertakes to present every aspect of social life in America. It has more over the special purpose of comprehensing the inter-relationships between these separate social compartments, and determining what social changes are taking place. Not only are these changes to be ascertained but the attempt made to grasp their trend, or in other words, to grasp the law determining these changes. G. seeks to show in a criticism of the results and methods of this „collective expression of sociological research in the United States“, that notwithstanding the extraordinary experience these 40 leading social scientists could draw upon, and the admirable comprehensiveness of this work-indeed an encyclopedia of American social life-, the scientific aim was not achieved, and could not be achieved. This is due to the insufficiency of Ogburn’s theory which underlies the work, that phenomena of crisis are to be traced to the disproportionate rates of change of the various provinces of social life. It presupposes a relatively stable social order in which upheavals are felt as mere oscillations around an intrinsically firm nucleus. Because the fundamental phenomenon of the economic crisis is not considered, the Report dispenses with the approach to a methodological standpoint, according to which all social processes are decisively determined by economic processes. Another important objection, which G. illustrates by a series of examples relates to concept of the trend borrowed from the business cycle. This can in no way furnish a suitable social law, because it tends to resolve all qualitative social relationships into mathematical- statistical formulae. Present day society, with its manifold divisions, can never be understood by quantitative methods only, but presumes a dialectical point of view for social life as a whole, which is ever in a state of flux. Since such a theoretical aim vitiated, but even its practical proposals, which it puts forward to rectify the shortcomings of American social life, fail to touch the root of the evil. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 62.1 (2001) 59-79 [Access article in PDF] Money and Sovereignty in Early Modern France Jotham Parsons [The mint official] must above all seek integrity in the moneys, on which our features are imprinted and on which the general good depends. For what would be safe if our image were offended, and if that which a subject ought to venerate in his heart were (...) immediately violated by a sacrilegious hand? 1Early modern French commentators on money and monetary policy were fond of quoting this very late antique chancery formula; 2 it even appears in the epigraph to one unpublished commonplace book on the subject from the early seventeenth century. 3 Its popularity was no doubt due partly to the fact that classical literature contained few other theoretical statements on the practicalities of issuing money. 4 It also showed how deeply classical humanism had shaped economic thought, as it had done to all of French political culture. This was apparent as early as 1514 in Guillaume Budé's scholarly classic, De Asse et partibus ejus. 5 By 1600 these influences had ensconced themselves so firmly that economic writers found it nearly impossible to talk about money without a [End Page 59] full panoply of classical erudition. 6 In France the second half of the sixteenth century saw the rise of a specialized, expert, and increasingly systematic tradition of monetary thought. Despite its classical vocabulary, this economic literature was in many ways "modern" in its methods, ambitions, and subject. While developing an account which aspired to a scientific explanation of commercial society and of how government and money interacted, the French commentators came to a partial realization of how radically their own society differed from those which had gone before. In this respect the prevailing climate of thought about money influenced even a writer as non-technical as Michel de Montaigne.Traditionally, scholarly treatment of early modern French economic texts has focused on a relatively small range of issues and authors. One such issue, the origins of the "quantity theory of money" (with Jean Bodin as its hero), is notable for its sterility, since that concept was not and could not have been meaningful to contemporaries. 7 The origin and development of "mercantilism" or, more broadly, of "political economy" in general, has proven a more fruitful subject of inquiry. 8 Undeniably, the changing relationships among governments, merchants, and the economy were a major public issue and, in the seventeenth century, a major site of theoretical reflection on the nature of political power generally. Even so, an excessive concentration on mercantilism is dangerous, for however one defines it, it was not the first, and for a long time not the most significant, economic discourse in France. Rather, from the 1560s well into the seventeenth century, French discussions of economic issues centered on very concrete problems brought about by the government's obligation to issue and maintain a stable currency. 9 While one would search this literature in vain for the specific doctrines of modern economics, I argue that it did represent a real achievement in the early modern understanding of commerce and the state. Though they have not received their due from scholars, the writers who took part in these debates formed a large and influential school with close ties to the actual institutions of government. 10 The French monetary theorists did an enormous amount [End Page 60] to set the stage for the mercantilist era. They developed a detailed notion of monetary economics as a specialized discipline, and above all they placed money and economic policy in the context of a multi-national system of commercial states. In so doing, they sought to comprehend and control not just money but the modern state itself.Early modern money was perched uncomfortably between commodity and fiat. Bewildering varieties of coins circulated, composed of all sorts of alloys. The government assigned a face value for each coin which it authorized to circulate in the abstract accounting unit called the "money of account." 11 This value was almost always greater than... (shrink)

This paper is concerned with extensions of geometric stability theory to some nonelementary classes. We prove the following theorem:Theorem. Let [Formula: see text] be a large homogeneous model of a stable diagram D. Let p, q ∈ SD(A), where p is quasiminimal and q unbounded. Let [Formula: see text] and [Formula: see text]. Suppose that there exists an integer n < ω such that [Formula: see text] for any independent a1, …, an∈ P and finite (...) subset C ⊆ Q, but [Formula: see text] for some independent a1, …, an, an+1∈ P and some finite subset C ⊆ Q.Then [Formula: see text] interprets a group G which acts on the geometry P′ obtained from P. Furthermore, either [Formula: see text] interprets a non-classical group, or n = 1,2,3 and•If n = 1 then G is abelian and acts regularly on P′.•If n = 2 the action of G on P′ is isomorphic to the affine action of K ⋊ K* on the algebraically closed field K.•If n = 3 the action of G on P′ is isomorphic to the action of PGL2(K) on the projective line ℙ1(K) of the algebraically closed field K.We prove a similar result for excellent classes. (shrink)

The main results in the paper are the following. Theorem A. Suppose that T is superstable and M ⊂ N are distinct models of T eq . Then there is a c ϵ N⧹M such that t is regular. For M ⊂ N two models we say that M ⊂ na N if for all a ϵ M and θ such that θ ≠ θ , there is a b ∈ θ ⧹ acl . Theorem B Suppose that T is (...) superstable , M ⊂ na N are models of T eq , and p is a regular type non-orthogonal to t . Then there is a c ϵ N such that t is regular and non-orthogonal to p. Furthermore, there is a formula θ ∈ t such that a ∈ θ and t ⊥ ̷ p ⇒ t is regular. We used these results to obtain ‘good’ tree decompositions of models in superstable theories with NDOP. See Definition 5.1 for the undefined terms. Theorem C Suppose that T is superstable with NDOP and M ⊨ T eq . Then every ⊂ na - decomposition inside M extends to a ⊂ na -decomposition of M. Furthermore, if 〈N η , a η : η ∈ I〉 is any ⊂ na -decomposition of M, then M is minimal over ∪N η and for all η ∈ I. M is dominated by ∪N η over N η . Using some stable group theory we show that when Th is superstable with NDOP and 〈 N η : η ∈ I 〉 is a tree decomposition of M, then M is constructible over ∪ n η with respect to a very strong isolation relation. (shrink)

This paper applies a proposed modified stochastic fractal search algorithm (MSFS) for dealing with all constraints of optimal reactive power dispatch (ORPD) and finding optimal solutions for three different cases including power loss optimization, voltage deviation optimization, and L-index optimization. The proposed MSFS method is newly constructed in the paper by modifying three new solution update mechanisms on standard stochastic fractal search algorithm (SSFS). The first modification is to keep only one formula and abandon one formula in the (...) diffusion process while the second modification and the third modification are used in the first update and the second update. In two updates of SSFS, solutions with low quality are updated with high probability while other solutions with high quality do not get chances to be updated. This manner results in the fact that some promising solutions around the high quality solutions can be missed. In order to tackle this restriction, the second modification of MSFS is to newly update the worst solutions in the first update and the best solutions in the second update. In the third modification, all existing formulas of SSFS in the two updates are abandoned and the same new proposed technique is used for updating such solutions in two updates. Compared to SSFS, the three modifications can bring advantages to MSFS such as using smaller number of produced solutions per iteration, spending shorter execution time, finding better optimal solutions, and owning more stable search ability. Furthermore, the proposed method also sees its effectiveness and robustness over SSFS by testing on IEEE 30-bus system and IEEE 118-bus system with three different single objectives for each system. The proposed method can find less minimum, average, and maximum for all the cases in addition to faster search speed. Besides, the proposed method is also compared to other methods such as PSO-based method group, GA-based method group, DE-based method group, and other recent methods. Result comparisons also indicate that the proposed method can be more efficient than almost all these methods with respect to less minimum and smaller values of control parameters. As a result, evaluation of the performance of the proposed method is that it should be used for seeking solutions of ORPD problem. (shrink)

Economists typically assume that preferences are fixed-that people know what they like and how much they like it relative to all other things, and that this rank-ordering is stable over time. But this assumption has never been accepted by any other discipline. Economists are increasingly having difficulty arguing that the assumption is true enough to generate useful predictions and explanations. Indeed, law and economics scholars increasingly acknowledge that preferences are constructed, and that the law itself can help construct preferences. (...) Still, fixed preferences are often treated as a normative ideal: Even if people don't have fixed preferences, they should. Behavioral law and economics scholars offer approaches to deal with this normative shortcoming. My article argues that preference construction, properly understood, is not normatively undesirable. Having fixed preferences means having a complete and stable rank ordering of what we want that dictates our choices. But we often do not have such an ordering, and rationally so. My article argues instead for an alternative process-based, account of preference construction. Rather than having a complete rank ordering, we have ways of making choices. We construct narratives, using evaluative criteria against a backdrop of wants, desires and inclinations, some of which we rank order and some of which we do not. The evaluative criteria embed a consideration of transaction costs: critically, where a decision is not very consequential, a formulaic decision rule that permits a ready choice among roughly comparable alternatives may serve our purposes better than a more considered alternative-by-alternative assessment. Our wants, desires and inclinations are for both traditional objects of choice and higher order values and desires; they are both previously constructed and constructed and elicited in the choice-making process. My article makes the case for such an account's potential explanatory power, as well as its tractability. (shrink)

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing (...) when justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge. (shrink)

Alguns autores têm afirmado que o externalismo semântico de Putnam implica em um tipo de essencialismo que não descreve adequadamente a prática científica, já que as referências dos termos que designam espécies naturais seriam determinadas por características essenciais dos exemplares que compõem cada uma daquelas espécies. Essas essências seriam as verdadeiras responsáveis pela identidade das espécies naturais. Uma vez conhecidas tais essências, estaríamos aptos a identificar tais espécies em qualquer mundo possível, visto que suas essências permaneceriam estáveis mesmo diante de (...) mudanças nas descrições de outros de seus atributos. Logo, o externalismo semântico parece inadequado para explicar o desenvolvimento da ciência. Ademais, os critérios de identificação de espécies químicas e biológicas não são fixados da maneira proposta por Putnam. Este artigo apresenta essas objeções ao externalismo semântico de Putnam e formula uma resposta, afirmando que Putnam não postulou uma tese própria sobre critérios de identidade para espécies naturais. Sustenta-se que as menções de Putnam a postulados científicos são melhor compreendidas se interpretadas como elementos adicionais para a determinação das referências de termos que designam espécies naturais.Abstract:Some authors have argued that Putnam’s semantic externalism entails a kind of essentialism which does not describe scientific practice adequately, since the references of the terms that designate natural kinds would be determined by essential traits of the specimens which make up those natural kinds. Those essences would account for the identity of natural kinds. Once such essences are known, we would be able to identify natural kinds in anypossible world, since such essences would remain stable even in the face of abrupt changes in the descriptions of other kinds’ attributes. Therefore, semantic externalism seems inadequate for accounting the development of science. Furthermore, the identification criteria for chemical and biological species are not determined in the mannerproposed by Putnam. This paper presents those criticisms to Putnam’s semantic externalism and formulates a reply, stating that Putnam did not posit a thesis on identity criteria for natural kinds. His Putnam’ references to scientific postulates are better understood when interpreted as additional elements for the determination of thereferences of natural kind terms.Keywords: Essentialism; Reference; Necessity; Natural kinds; Meaning; Hilary Putnam. (shrink)

This article is devoted to describing results of conceptualization of the idea of mind at the stage of maturity. Delineated the acquisition by the energy system (mind) of stable morphological characteristics, which associated with such a pivotal formation as the discourse. A qualitative structural and ontological sign of the system transition to this stage is the transformation of the verbal morphology of the mind into a discursive one. The analysis of the poststructuralist understanding of discourse in the context of (...) the dispersion of meanings (Foucault) made it possible to formulate a notion of it as a meaning that is constituted by the relation between the discursive practice and the worldview, regarded as a meta-discourse or a global discursive formation. In consequence of this relationship, a discrete and simultaneous scattering of meanings arises, the procedural side of which is a concrete discourse, and its productive aspect is linked with the creation of a local discursive formation. Based on this view it is proposed a logical formula of discourse, which takes into account the entropy of the language and the entropy of the worldview, as a particular manifestation of the mind entropy. Using this formula and considering the reactive nature of discourse, it was developed a classification, which included such types of discourses as reactive, suggestive, synthetic and creative. In turn, the proposed types of discourses are correlated with the specific characteristics of certain activities, as a psychological category. Also, it was considered the translation of the structure of discourse dissipation from the cognitive plan into the affective sphere because of which it is formed a hierarchy of significances, which performs the sense-forming function. It was analyzed the inverse influence of the hierarchy of significances on the structure of meanings dispersion and for respective account it was introduced a conditional coefficient of the value deviation of the significance of the meanings. This parameter reflects the sense correction of the meaning that occurs in the process of the emergence of discourse from discursive practice. Thus, the discourse is presented as a complex dynamic formation of the mind arising at the maturity stage of the system as a result of the combined effect of entropic dispersion of meanings and the value deviation of their significances. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Appreciating Susan SontagFred RushMuch education from the mid-1960s to the mid-1970s was self-education. Although one might happen to take a university course that incorporated contemporary art and criticism, it was a rarity. More often one supplemented university fare with one's own reading, listening, and viewing of cutting-edge art, anthropology, music, philosophy, linguistics, etc. Susan Sontag was for many Americans of that time a preeminent guide in this process, opening (...) doors to some of the most interesting and influential European work in art and criticism. Sontag's essayistic output—and she was one of the supreme writers in that genre—was seminal. Any sociologist or intellectual historian of the period would have to take her work greatly into account. Her incisive takes on her subject matter were not for everyone. Although trained as a philosopher at the then epicenter of the Anglophone philosophical world, Harvard, she did not tiptoe through academic complexities and was, therefore, decidedly out of step with the philosophical temperament of that time. She strode in, proselytized for her favorites, excoriated her enemies, and left no one in the room ignorant of the fact that she had been there, dominated the conversation and, on the way out, rearranged the furniture.Sontag's views generally have not received much philosophical attention. Even those who prize her critical work have tended to sell short the early, programmatic essays like "Against Interpretation" and "On Style." Perhaps this neglect is self-wrought. Sontag is often at her best when engaged in what one might call first-order criticism, that is, criticism of particular works of art on their own terms. Her work in critical theory tends to be both abstracting and declamatory and, so, operates against her strong suit. Moreover, Sontag's theory of criticism commits her to [End Page 36] the precedence of critical practice over theorizing. Accordingly, she is led to reduce the importance of those early essays. Yet this is where the interest of philosopher will fall, if indeed it falls at all.Sontag's main concern relevant to the philosophy of literature and to aesthetic theory more broadly is what she takes to be the colonization of aesthetic and critical response by what she terms "theory." Critical response is always, to some degree theoretical of course, so her point cannot be one that is ascribed sometimes to her, i.e., that critical response is supposed to be non-theoretical tout court. An "erotics of art," the famous formula contained in the last sentence of "Against Interpretation," is after all an erotics, which was in the ancient world a genre of theoretical investigation, not erotic experience or even erotica. Criticism can be theoretical in many senses as well. By itself the term "theory" does not rule out much unless one appends to it constraints having to do with the internal structure of bodies of knowledge that either qualify or disqualify them as theories correctly so-called. Sontag seems most concerned about two aspects of theoretical accounts of art: (A) their systematicity and (B) their use of modes of interpretation that undercut the aesthetic nature of works. With regard to (B), she is wary particularly of accounts of literary value that appeal to unconscious or subterranean social forces as determinative of meanings of works. The problem with (A) is that systematicity, she claims, tends toward exclusion and reduction, destroying the particularity of individual works.These two contentions comprise the diagnostic and negative side of Sontag's programmatic work in literary theory, i.e., what is to be avoided in one's experience and judgment of art. What is to be avoided is "interpretation," but what is interpretation exactly? What is the scope of Sontag's claim against it? Do her early essays provide a stable, convincing account of the relation between theory, on the one hand, and experience and criticism, on the other? Is she caught between formalism and a more politically engaged kind of criticism? On the positive side, what kind of critical response to literature is appropriate to its aesthetic nature? Is Sontag's replacement for interpretation viable? Sontag presents her answers to the first set of questions in an unstructured... (shrink)

A theory in natural science is a comprehensive formula or doctrine which describes and correlates in a unified abstract form of statement the general determining factors of some special group of natural facts. It is at once inclusive, realistic and understandable. If a theoretical statement holds good, the existence and characteristics of many individual events can be inferred deductively from it. It thus gives a logical basis for empirical fact. But it is based on experience of nature, and must (...) conform to the facts of nature; these are primary, and a valid theory, no matter how broad it may be, is to be considered as itself a statement of fact, i.e., a true description of some condition which has a real and stable existence in the natural world. In its scientific usage, the term “fact” refers primarily to some datum of experience having the special character of permanence or regular recurrence; this is why scientific facts are verifiable; in this respect they differ from the passing individual events of history. Any scientific theory presupposes the stability and unequivocality of the natural facts. Hence if a theory is sound, it furnishes a reliable basis for prediction, discovery and invention. Scientific or technological creation then becomes possible; modern engineering and medicine could never have become what they are without a background of theoretical physics and biology. Obviously any natural science must always have at its disposal an ample body of observational and experimental data, but in most cases the work of collecting and verifying these is carried out under the guidance of theory. (shrink)

John Dewey looks to the Nicomachean Ethics of Aristotle for the general outlines of his ethical thought. In his 1932 Ethics, he describes the ethical framework that he shares with Aristotle in terms of knowledge, choice and character: "The formula was well stated by Aristotle. The doer of the moral deed must have a certain 'state of mind' in doing it. First, he must know what he is doing; secondly, he must choose it, and choose it for itself, and (...) thirdly, the act must be the expression of a formed and stable character."1 This paper examines the interaction of these elements within Aristotle's and Dewey's ethical thought. In particular, it discusses the idea of the good as a link between the character virtues and practical deliberation. It will show how this idea of the good that guides practical deliberation is also an expression of one's character virtues. (shrink)

We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies. The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.

Image factorizations in regular categories are stable under pullbacks, so they model a natural modal operator in dependent type theory. This unary type constructor [A] has turned up previously in a syntactic form as a way of erasing computational content, and formalizing a notion of proof irrelevance. Indeed, semantically, the notion of a support is sometimes used as surrogate proposition asserting inhabitation of an indexed family. We give rules for bracket types in dependent type theory and provide complete semantics (...) using regular categories. We show that dependent type theory with the unit type, strong extensional equality types, strong dependent sums, and bracket types is the internal type theory of regular categories, in the same way that the usual dependent type theory with dependent sums and products is the internal type theory of locally Cartesian closed categories. We also show how to interpret first-order logic in type theory with brackets, and we make use of the translation to compare type theory with logic. Specifically, we show that the propositions-as-types interpretation is complete with respect to a certain fragment of intuitionistic first-order logic, in the sense that a formula from the fragment is derivable in intuitionistic first-order logic if, and only if, its interpretation in dependent type theory is inhabited. As a consequence, a modified double-negation translation into type theory (without bracket types) is complete, in the same sense, for all of classical first-order logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 697 Excellent as Sullivan's book is, it has raised a host of questions which, though it cannot be fairly expected to discuss them at length, much less to resolve, are at the heart of ongoing reflections about the possibility of salvation outside the visible Church. Such questions concern the concrete ways in which God works in the lives of peoples of different religions, the unique and normative (...) role of Christ in the history of salvation, the function of non-Christian religions as mediations of salvation, and so on. And the debate on these issues rages on among Catholic as well as non-Catholic theologians! One wishes that Sullivan had given a fuller account of this debate which is central in interreligious dialogue. More directly connected with the method and approach of the book itself are the questions of dogmatic development and the hermeneutics of doctrines. To put it more concretely, was Leonard Feeney, with whose ironic fate the book opens and ends, simply expressing the ancient doctrine of the deposit of the faith concerning salvation in the Church in a negative and imperfect fashion? Or was he (and more importantly, popes and official teachers of the faith) wrong in affirming the exclusiveness implicit in the formula extra ecclesiam nulla salus (which apparently they did)? H the latter, then the issues of infallible magisterium and dogmatic ' development ' raise their ugly heads, and one has to come to terms with them. The Catholic University of America Washington, D.C. PETER c. PHAN Character. By JOEL KUPPERMAN. Oxford: Oxford University Press, 1991. Pp. vi + 193. The two theses of J. Kupperman's Character are "that character is of central importance to ethics and that ethical philosophy will have to be restructured once this is understood " (p. 3). The argument has three stages: the first three chapters explicate the notion of character and its relationship to the notions of the self and of responsibility; the next two consider the dominant, rival theories in contemporary ethics; the last two address the topics of value and the place of character in ethics. In two appendices, Kupperman applies the substantive conclusions of the work to the issues of moral psychology and the education of character. A brief review cannot communicate the many nuances of argument and the precise and lucid style that distinguish the book. While certain parts of the argument seem problematic, or at least in 698 BOOK REVIEWS need of further development, the work deserves the attention of professional ethicists and of inquisitive non-professionals. The opening chapter offers the following definition of character: "X's character is X's normal pattern of thought and action, especially with respect to concerns and commitments in matter affecting the hap· piness of others or of X, and most especially in relation to moral choices" (p. 17). In the second chapter, Kupperman considers three views: Enduring Self (ES), No Self (NS), and Constructed Self (CS). The ES appears to be seH-evidently true. But what exactly is the self and where is it to he found? It is difficult to fix the abiding " I " amid or behind the flux of our self-experience. On the other hand, even Hume's skepticism concerning the self presumes that " we know where to look " for it. The " I " is simultaneously obvious and elusive, stable and unstable (p. 40). Thus, both the ES and the NS are problematic, The third option is the Constructive Self, Kupperman holds that, as children, we begin with a "protoseH." The full-fledged self is often the result of orientations, habits, and traits of character developed before one has even begun deliberating about the kind of character one would like to have. Like the self, character is constructed mostly through unreflective choices. But this raises questions about responsibility, which is the focus of the third chapter. If we have not willed to be the sorts of persons we now are, how can we be held responsible for who we are or what we do? Actions do not " flow from character like water from a pipe " (p, 59). Over long periods of time and through a reorganization of large portions of our life, we can... (shrink)

We extend our general approach to characterizing information to multi-agent systems. In particular, we provide a formal description of an agent''s knowledge containing exactly the information conveyed by some (honest) formula . Only knowing is important for dynamic agent systems in two ways. First of all, one wants to compare different states of knowledge of an agent and, secondly, for agent a''s decisions, it may be relevant that (he knows that) agent b does not know more than . There (...) are three ways to study the question whether a formula can be interpreted as minimal information. The first method is semantic and inspects minimal models for (with respect to some information order on states). The second one is syntactic and searches for stable expansions, minimal with respect to some language *. The third method is a deductive test, known as the disjunction property. We present a condition under which the three methods are equivalent. Then, we show how to construct the order by collecting layered orders. Focusing on the multi-agent case we identify languages * for various orders , and show how they yield different notions of honesty for different multi-modal systems. We then provide several tools for studying honesty types and illustrate their usefulness on a number of examples, for three modal systems of particular interest. Finally, we relate the different notions of minimal knowledge, and describe possible patterns of honesty for these systems. (shrink)

The paper begins with a conceptual discussion of Michael Dummett's proof-theoretic justification of deduction or proof-theoretic semantics, which is based on what we might call Gentzen's thesis: 'the introductions constitute, so to speak, the "definitions" of the symbols concerned, and the eliminations are in the end only consequences thereof, which could be expressed thus: In the elimination of a symbol, the formula in question, whose outer symbol it concerns, may only "be used as that which it means on the (...) basis of the introduction of this symbol".' The intuitive philosophical content of Dummett's notions of harmony and stability is that harmony obtains if the grounds for asserting a proposition match the consequences of accepting it, and stability obtains if the converse also holds. Rules of inference define the meanings of a logical constant they govern if and only if they are stable. Gentzen observed that 'it should be possible to establish on the basis of certain requirements that the elimination rules are functions of the corresponding introduction rules.' One of the objectives of this paper is to specify such a function: I will specify a process by which it is possible to determine the elimination rules of logical constants from their introduction rules, and conversely, to determine the introduction rules from the elimination rules. I'll give the general forms of rules of inference and generalised reduction procedures for the normalisation of deduction. I'll give a formally precise characterisations of harmony and stability and show that deductions in logics that contain only constants governed by stable rules always normalise. (shrink)

We prove two results on the stability spectrum for Lω1,ω. Here [Formula: see text] denotes an appropriate notion of Stone space of m-types over M. Theorem for unstable case: Suppose that for some positive integer m and for every α μ, K is not i-stable in μ. These results provide a new kind of sufficient condition for the unstable case and shed some light on the spectrum of strictly stable theories in this context. The methods avoid the (...) use of compactness in the theory under study. In this paper, we expound the construction of tree indiscernibles for sentences of Lω1,ω. Further we provide some context for a number of variants on the Ehrenfeucht–Mostowski construction. (shrink)

Farmers’ entrepreneurship is a powerful breakthrough for solving the problems associated with “agriculture, rural areas and farmers.” Although studies have commonly used the same entrepreneurial activities to analyze farmers’ entrepreneurship, its deep economic roots have rarely been investigated. Investigating the internal development mechanism within the same industry is helpful for understanding farmers’ entrepreneurship motivation and decision making and is an important point at which to implement regional research and enrich the overall research on farmers’ entrepreneurship in the Chinese context. Based (...) on a single-case study in Q Village, Fujian Province, this work identifies the key role played by relational contracts in entrepreneurship groups: reducing transaction costs, promoting investment in asset specificity, and improving contract flexibility. Moreover, this approach is conducive for different action groups in terms of stimulating entrepreneurial motivation in the initial entrepreneurship period and improving entrepreneurship learning ability in the long term. Primary Action Group transforms exploratory intuitive learning into exploratory compilation learning, and Secondary Action Group triggers the learning effect and makes a proprietary investment by utilizing intuitive formulaic learning and compiled formulaic learning, thus reducing unforeseen, contracting and verification costs. During the pattern maturity period, Primary Action Group rationally integrates the supply chain and forms a stable entrepreneurial paradigm, while Secondary Action Group does so to maintain prior information reserves and lower information search, supervised execution, and bargaining decision costs. The value cocreation ability of the same type of commercial modularity is formed, and the whole process of farmers’ entrepreneurship is completed. Our results have important implications for policymakers in China and other countries with clans. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

In [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], Hrushovski and the authors proved, in a certain finite rank environment, that rigidity of definable Galois groups implies that [Formula: see text] has the canonical base property in a strong form; “internality to” being replaced by “algebraicity in”. In the current paper, we give a reasonably robust definition of the “strong canonical base property” in a rather more general finite rank (...) context than [E. Hrushovski, D. Palacín and A. Pillay, On the canonical base property, Selecta Math. (N.S.) 19(4) (2013) 865–877], and prove its equivalence with rigidity of the relevant definable Galois groups. The new direction is an elaboration on the old result that [Formula: see text]-based groups are rigid. (shrink)

This paper analyses the rise of synthetic nitrogen in Great Britain and its empire, from the First World War to the aftermath of the Second World War. Rather than focus solely on technological innovations and consumption statistics, it seeks to explain how nitrogen was a central element in the expansion of a form of agricultural governance, which needed simplified, stable, and seemingly universal input/output formulae. In the first half of the twentieth century, nitrogen was thus gradually constructed as a (...) global indicator of development, as it was particularly adapted to scientific and political regimes increasingly relying upon abstraction and quantification. Yet, the history of nitrogenous fertilizers in the interwar years also shows that this cannot be reduced to a simple story of triumphant modernity, as their development and globalization was imperfect, unstable, accompanied by resistance and the resilience or emergence of other models. Rather than assuming an all-powerful “state” project, the paper thus seeks to recover the multiplicity of actors, and attempts to account for the rise of nitrogenous fertilizers; not just as the progressive application of a technological breakthrough, but as a difficult process embedded in technological, financial, and military constraints, corporate strategies, political imperatives, and the changing institutional framework of agricultural research. (shrink)

_Edusemiotics_ addresses an emerging field of inquiry, educational semiotics, as a philosophy of and for education. Using "sign" as a unit of analysis, educational semiotics amalgamates philosophy, educational theory and semiotics. Edusemiotics draws on the intellectual legacy of such philosophers as John Dewey, Charles Sanders Peirce, Gilles Deleuze and others across Anglo-American and continental traditions. This volume investigates the specifics of semiotic knowledge structures and processes, exploring current dilemmas and debates regarding self-identity, learning, transformative and lifelong education, leadership and policy-making, (...) and interrogating an important premise that still haunts contemporary educational philosophy: Cartesian dualism. In defiance of substance dualism and the fragmentation of knowledge that still inform education, the book offers a unifying paradigm for education as edusemiotics and emphasises ethical education in compliance with the semiotic unity between knowledge and action. Chapters contain accessible discussions in the context of educational philosophy and theory, crossing the borders between logic, art, and science together with a provocative theoretical critique. Recently awarded a PESA book award for its contribution to the philosophy of education, _Edusemiotics_ will appeal to an academic readership in education, philosophy and cultural studies, while also being an inspiring resource for students. (shrink)