In model theory, a branch of mathematical logic, we can classify mathematical structures based on their logical complexity. This yields the so-called stability hierarchy. Independence relations play an important role in this stability hierarchy. An independence relation tells us which subsets of a structure contain information about each other, for example, linear independence in vector spaces yields such a relation.Some important classes in the stability hierarchy are stable, simple, and NSOP $_1$, each being contained (...) in the next. For each of these classes there exists a so-called Kim-Pillay style theorem. Such a theorem describes the interaction between independence relations and the stability hierarchy. For example, simplicity is equivalent to admitting a certain independence relation, which must then be unique.All of the above classically takes place in full first-order logic. Parts of it have already been generalised to other frameworks, such as continuous logic, positive logic, and even a very general category-theoretic framework. In this thesis we continue this work.We introduce the framework of AECats, which are a specific kind of accessible category. We prove that there can be at most one stable, simple, or NSOP $_1$ -like independence relation in an AECat. We thus recover (part of) the original stability hierarchy. For this we introduce the notions of long dividing, isi-dividing, and long Kim-dividing, which are based on the classical notions of dividing and Kim-dividing but are such that they work well without compactness.Switching frameworks, we generalise Kim-dividing in NSOP $_1$ theories to positive logic. We prove that Kim-dividing over existentially closed models has all the nice properties that it is known to have in full first-order logic. We also provide a full Kim-Pillay style theorem: a positive theory is NSOP $_1$ if and only if there is a nice enough independence relation, which then must be given by Kim-dividing.Abstract prepared by Mark Kamsma.E-mail:mark@markkamsma.nl.URL:https://markkamsma.nl/phd-thesis. (shrink)

In a simple CM-trivial theory every hyperimaginary is interbounded with a sequence of finitary hyperimaginaries. Moreover, such a theory eliminates hyperimaginaries whenever it eliminates finitary hyperimaginaries. In a supersimple CM-trivial theory, the independence relation is stable.

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)

The classes stable, simple, and NSOP $_1$ in the stability hierarchy for first-order theories can be characterised by the existence of a certain independence relation. For each of them there is a canonicity theorem: there can be at most one nice independence relation. Independence in stable and simple first-order theories must come from forking and dividing (which then coincide), and for NSOP $_1$ theories it must come from Kim-dividing. We generalise this work to (...) the framework of Abstract Elementary Categories (AECats) with the amalgamation property. These are a certain kind of accessible category generalising the category of (subsets of) models of some theory. We prove canonicity theorems for stable, simple, and NSOP $_1$ -like independence relations. The stable and simple cases have been done before in slightly different setups, but we provide them here as well so that we can recover part of the original stability hierarchy. We also provide abstract definitions for each of these independence relations as what we call isi-dividing, isi-forking, and long Kim-dividing. (shrink)

Journal of Mathematical Logic, Ahead of Print. We study classes of modules closed under direct sums, [math]-submodules and [math]-epimorphic images where [math] is either the class of embeddings, RD-embeddings or pure embeddings. We show that the [math]-injective modules of theses classes satisfy a Baer-like criterion. In particular, injective modules, RD-injective modules, pure injective modules, flat cotorsion modules and [math]-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)

In this paper we study elementary submodels of a stable homogeneous structure. We improve the independence relation defined in Hyttinen 167–182). We apply this to prove a structure theorem. We also show that dop and sdop are essentially equivalent, where the negation of dop is the property we use in our structure theorem and sdop implies nonstructure, see Hyttinen.

We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent theories.

Multimodal neuroimaging provides a rich source of data for identifying brain regions associated with disease progression and aging. However, present studies still typically analyze modalities separately or aggregate voxel-wise measurements and analyses to the structural level, thus reducing statistical power. As a central example, previous works have used two quantitative MRI parameters—R2* and quantitative susceptibility —to study changes in iron associated with aging in healthy and multiple sclerosis subjects, but failed to simultaneously account for both. In this article, we propose (...) a unified framework that combines information from multiple imaging modalities and regularizes estimates for increased interpretability, generalizability, and stability. Our work focuses on joint region detection problems where overlap between effect supports across modalities is encouraged but not strictly enforced. To achieve this, we combine L1, total variation, and L2 group lasso penalties. While the TV penalty encourages geometric regularization by controlling estimate variability and support boundary geometry, the group lasso penalty accounts for similarities in the support between imaging modalities. We address the computational difficulty in this regularization scheme with an alternating direction method of multipliers optimizer. In a neuroimaging application, we compare our method against independent sparse and joint sparse models using a dataset of R2* and QS maps derived from MRI scans of 113 healthy controls: our method produces clinically-interpretable regions where specific iron changes are associated with healthy aging. Together with results across multiple simulation studies, we conclude that our approach identifies regions that are more strongly associated with the variable of interest, more accurate, and more stable with respect to training data variability. This work makes progress toward a stable and interpretable multimodal imaging analysis framework for studying disease-related changes in brain structure and can be extended for classification and disease prediction tasks. (shrink)

The bilateral relationship between China and Myanmar is important and intricate despite being asymmetrical in China's favour. Whereas most observers regard the relationship as being heavily weighted in China's favour, Myanmar does have a fair amount of latitude within the relationship that is informed by historical, economic, and strategic considerations. The nationalism and xenophobia present in the attitudes of elite from the Myanmar military junta is both recognized and understood by China that is keen to have a stable peripheral (...) environment. There are also important security issues such as the ethnic armies that currently have a ceasefire arrangement with the junta along the border areas that need to be resolved in a coordinated fashion to prevent negative spillage into China. In light of such special idiosyncratic and terrain considerations, Myanmar wields relative independence within this asymmetrical relationship. (shrink)

An option available to an agent is stable if it maximizes expected utility on the hypothetical assumption that the agent is going to choose it. As is well known, some decision problems lack a stable solution. Paul Weirich (1986 and 1988) has recently proposed a decision principle which prescribes that the option chosen should be at least weakly stable--or "weakly ratifiable", to use his terminology. According to him, full stability is an excessively strong demand. I shall argue (...) that Weirich's proposal conflicts with the familiar condition of dominance. But I shall also prove that this difficulty can be avoided if we replace weak stability by "moderate" stability--where the latter property is somewhat stronger than the former. It will be seen, however, that this modification does not help against other ailments connected with stability. In particular, to heed the demand of stability (of any kind) is to engage in a form of "wishful acting". Also, the different stability demands all conflict with a close relative of the dominance condition: the condition of "indifference". According to this condition, two actions are equally choiceworthy if they would always lead to the same outcomes--whatever state the world is in. On the other hand, the conditions of dominance and indifference would both be satisfied if we replaced a demand for stability (of some kind) by a related but distinct principle of "retrievability". Retrievability and (full) stability are mutually independent properties of options, but each of them entails moderate stability. The paper ends with a discussion of the relevance of retrievability to theories of choiceworthiness and practical reason. (shrink)

Fisher [10] and Baur [6] showed independently in the seventies that if T is a complete first-order theory extending the theory of modules, then the class of models of T with pure embeddings is stable. In [25, 2.12], it is asked if the same is true for any abstract elementary class $(K, \leq _p)$ such that K is a class of modules and $\leq _p$ is the pure submodule relation. In this paper we give some instances where this (...) is true:Theorem.Assume R is an associative ring with unity. Let $(K, \leq _p)$ be an AEC such that $K \subseteq R\text {-Mod}$ and K is closed under finite direct sums, then: •If K is closed under pure-injective envelopes, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda \geq \operatorname {LS}(\mathbf {K})$ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•If K is closed under pure submodules and pure epimorphic images, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.•Assume R is Von Neumann regular. If $\mathbf {K}$ is closed under submodules and has arbitrarily large models, then $\mathbf {K}$ is $\lambda $ -stable for every $\lambda $ such that $\lambda ^{|R| + \aleph _0}= \lambda $.As an application of these results we give new characterizations of noetherian rings, pure-semisimple rings, Dedekind domains, and fields via superstability. Moreover, we show how these results can be used to show a link between being good in the stability hierarchy and being good in the axiomatizability hierarchy.Another application is the existence of universal models with respect to pure embeddings in several classes of modules. Among them, the class of flat modules and the class of $\mathfrak {s}$ -torsion modules. (shrink)

The notion $J$ is independent in $(M,M_0,N)$ was established by Shelah, for an AEC (abstract elementary class) which is stable in some cardinal $\lambda$ and has a non-forking relation, satisfying the good $\lambda$-frame axioms and some additional hypotheses. Shelah uses independence to define dimension. Here, we show the connection between the continuity property and dimension: if a non-forking satisfies natural conditions and the continuity property, then the dimension is well-behaved. As a corollary, we weaken the stability hypothesis (...) and two additional hypotheses, that appear in Shelah's theorem. (shrink)

Rawls in his later philosophy claims that it is sufficient to accept political conception as true or right, depending on what one's worldview allows, on the basis of whatever reasons one can muster, given one's worldview (doctrine). What political liberalism is interested in is a practical agreement on the political conception and not in our reasons for accepting it. There are deep issues (regarding deep values, purpose of life, metaphysics etc.) which cannot be resolved through invoking common reasons (this is (...) the fact of free reason itself), and trying to resolve them would involve us in interminable debates and would hamper the practical task of agreement on the political conception. Given the absolute necessity of a political society which is stable and enduring, it is thus wise to avoid these issues in founding a political society and choosing its basic principles - this is the pragmatic part of Rawls's position. In this paper I argue that this strategy leads Rawls into a paradox: (i) although the intention is to stay independent of comprehensive doctrines, the political conception is in fact totally (and precariously) dependent on comprehensive doctrines (not just on one doctrine but on each and every major doctrine in society). It is dependent on them: for its conceptualisation as an independent idea, for its justification, for the check of its reasonability in relation to the external world, for the formation of identities and value inculcation and hence for the formation of its model citizen; (ii) the very search for independence makes the political conception more dependent on comprehensive doctrines, and by extension makes it potentially more prone to intervention in and tampering with comprehensive doctrines (it is enough to show that it is a strong conceptual possibility to cast doubt on the whole strategy). Thus, for example, the political conception relies on the hope that “firmly held convictions gradually change” and that it would “in fact . . . have the capacity to shape those doctrines toward itself”. The purpose of the Rawlsian conjecture is to give these “hopes” a concrete, practical form by giving advice to proponents of the comprehensive doctrine on how they can do all this and “try to show them that, despite what they might think, they can still endorse a reasonable political conception”. I further argue that this paradox can be overcome by making the core of political liberalism more flexible. (shrink)

We study a class of 0-categorical simple structures such that every M in has uncomplicated forking behavior and such that definable relations in M which do not cause forking are independent in a sense that is made precise; we call structures in independent. The SU-rank of such M may be n for any natural number n>0. The most well-known unstable member of is the random graph, which has SU-rank one. The main result is that for every strongly independent structure M (...) in , if a sentence φ is true in M then φ is true in a finite substructure of M. The same conclusion holds for every structure in with SU-rank one; so in this case the word ‘strongly’ can be removed. A probability theoretic argument is involved and it requires sufficient independence between relations which do not cause forking. A stable structure M belongs to if and only if it is 0-categorical, 0-stable and every definable strictly minimal subset of is indiscernible. (shrink)

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)

The democratic transformations that have taken place in our country since independence have laid the foundations for new state-church relations. The relations between the state and the Church in this situation have acquired fundamentally new qualities, which, unlike the past, are characterized by a generally stable partnership, mutual respect and cooperation. Such relations are enshrined in the Constitution of Ukraine, the Law of Ukraine "On Freedom of Conscience and Religious Organizations", other legislative acts and international legal agreements.

In lieu of an abstract, here is a brief excerpt of the content:Mother-Daughter Relations and the Maternal in Irigaray and ChodorowAlison StoneGod the Father and Jesus the Son; Abraham and Isaac; Uranus, Cronus, and Zeus; Zeus and Dionysus; Hamlet and his father; Fyodor Karamazov and his three sons—representations of and fantasies about father-son relationships are central to Western culture and philosophy. Within philosophy, one thinks of Hegel’s conception of the dialectic in terms of the divine trinity, Nietzsche’s preoccupation with Christ (...) and Dionysus, or Kierkegaard’s meditations on Abraham’s near-murder of Isaac. In contrast, mother-daughter relationships have been shrouded in near-universal silence—much more so than representations of either mothers and sons (Oedipus and Jocasta; Mary and Jesus) or fathers and daughters (Agamemnon and Iphigenia; Lear and Cordelia). Female and feminist theorists, writers, and artists have done much to bring mother-daughter relationships into representation and to reimagine the maternal beyond its traditional subservience to father-son dynasties.Amongst continental feminists, Luce Irigaray and Julia Kristeva have, of course, made major contributions to this task. Within Anglophone feminism, too, feminist psychoanalytic thinkers have sought to rectify Freud’s overemphasis on the paternal and on father-son relations. Nancy Chodorow’s important work in this area paints a portrait of contemporary mother-daughter relations which seems, at first sight, strikingly similar to Irigaray’s. Both thinkers suggest that mothers and their infant daughters experience a unique level of mutual identification. But under patriarchy—specifically, given exclusively female childrearing for Chodorow and given the absence of any symbolization of female subjectivity for Irigaray—daughters are forced to turn to the father [End Page 45] to achieve any psychical independence from their mothers. The independence that daughters thus attain coexists with ongoing psychical identification with their mothers, so that women oscillate endlessly between separation from and mergence with their mothers. If the dominant template for father-son relations involves violent rivalry followed by guilt-ridden father-worship as the cement of fraternal society, as Freud described in Totem and Taboo (Freud 2001), the template for mother-daughter relations involves hostile separation constantly undone by ongoing fusion. This difference in templates maps the social-symbolic difference between the paternal position of power/authority/law and the maternal position of powerlessness/silence/body.However, the manifest similarities between Irigaray’s and Chodorow’s pictures are embedded in deep theoretical differences. The details of their descriptions of mother-daughter relations differ, and they give different explanations for why these relations follow a logic of separation and fusion: female mothering for Chodorow, the paternal symbolic order for Irigaray. They make different proposals for how to change these relations: shared parenting for Chodorow versus symbolic transformation for Irigaray. They hold conflicting conceptions of the self and of language, reflecting their heterogeneous psychoanalytic backgrounds in Anglo-American object relations versus French Lacanianism and poststructuralism. These deep differences raise questions about whether Chodorow and Irigaray are discussing mother-daughter relations in the same sense at all.Bringing Irigaray and Chodorow together across their different intellectual contexts, this article compares and partially synthesizes their visions of the maternal and of mother-daughter relations. By integrating their perspectives, we can move beyond the “impasse” between Lacanian and object-relations feminisms that dominated psychoanalytic feminist debates in the 1980s and 1990s (Brennan 1991)—debates that have crucially shaped continental feminists’ orientation towards questions of sexual difference, language and representation, and the embodied psyche.The impasse in question has at least two strands. First, for object-relations feminists such as Chodorow, our pre-Oedipal relations with our mothers shape us so that we acquire “core” selves with a fairly stable gender. This approach elevates the mother in importance (compared to classical psychoanalysis with its emphasis on the father), but it loses sight of psychic and gender instability. This can make Chodorow’s views seem rather dated given the impact of Judith Butler’s work and her emphasis on the unstable, shifting nature of gender. Lacanian feminists such as Jacquelyn Rose (Rose 1986) reemphasize psychic instability, but they do so by stressing that the subject is split between paternal language and the pre-Oedipal maternal realm, which means that these theorists also... (shrink)

In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role (...) of the one-to-one correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis. (shrink)

We introduce Lascar strong types in excellent classes and prove that they coincide with the orbits of the group generated by automorphisms fixing a model. We define a new independence relation using Lascar strong types and show that it is well-behaved over models, as well as over finite sets. We then develop simplicity and show that, under simplicity, the independence relation satisfies all the properties of nonforking in a stable first order theory. Further, simplicity for (...) an excellent class, as well as the independence relation itself, is uniquely determined. Finally, we show that an excellent class is simple if and only if it has extensible U-rank . We deduce that any excellent class of finite U-rank is simple, and that any uncountably categorical excellent class has an expansion with countably many constants which is simple. (shrink)

Ukrainian lands in the twentieth and twenty-first centuries have been in proximity of great geopolitical changes several times. During that time the Ukrainian nation – due to various factors – encountered a number of “windows of opportunity” for achieving the realization of dreams about independence and national sovereignty. The author identified in the period considered four “general moments,” of which two have been completed successfully. The first of these occurred in 1990–1991, when for the first time in modern history, (...) Ukrainians managed to achieve a lasting and relatively stable independence. The second of the “moments” – still unresolved – are events that began in the late autumn of 2013. The process, called “Revolution of Dignity”, represents a new quality in the history of the Ukrainian nation, therefore, that the Ukrainians have to defend the status quo but not to seek to achieve an independent being. The analysis leads to the conclusion that the ability of Ukrainians to achieve and maintain independence is largely a function of the relative power of the Russian state as measured with respect to the shape and quality of international relations. (shrink)

Frequent independent origins of environmental sex determination (ESD) are assumed within amniotes. However, the phylogenetic distribution of sex‐determining modes suggests that ESD is likely very ancient and may be homologous across ESD groups. Sex chromosomes are demonstrated to be old and stable in endothermic (mammals and birds) and many ectothermic (non‐avian reptiles) lineages, but they are mostly non‐homologous between individual amniote lineages. The phylogenetic pattern may be explained by ancestral ESD with multiple transitions to later evolutionary stable genotypic (...) sex determination. It is pointed out here that amniote ESD shares several key aspects with sequential hermaphroditism of fishes such as a lack of sex differences in genomes, biased population sex ratios, and potentially also molecular mechanism related to general stress responses. Here, it is speculated that ESD evolves via a heterochronic shift of the sensitive period of sex change from the adult to the embryonic stage in a hermaphroditic amniote ancestor. Also see the video abstract here https://youtu.be/q2mjtlCefu4. (shrink)

We exhibit a bridge between the theory of cellular categories, used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the combinatorial cellular categories (those where, in a precise sense, the cellular morphisms are generated by a set) are exactly those that give rise to stable independence notions. We give two applications: on the one hand, we show that the abstract elementary classes of roots of Ext studied (...) by Baldwin–Eklof–Trlifaj are stable and tame. On the other hand, we give a simpler proof (in a special case) that combinatorial categories are closed under 2-limits, a theorem of Makkai and Rosický. (shrink)

A relation between two secrets, known in the literature as nondeducibility , was originally introduced by Sutherland. We extend it to a relation between sets of secrets that we call independence . This paper proposes a formal logical system for the independence relation, proves the completeness of the system with respect to a semantics of secrets, and shows that all axioms of the system are logically independent.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Citizens Without Sovereignty: Equality and Sociability in French Thought, 1670–1789Patrick HenryCitizens Without Sovereignty: Equality and Sociability in French Thought, 1670–1789, by Daniel Gordon; viii & 270 pp. Princeton: Princeton University Press, 1994, $39.50.Under examination here is the early modern period in France from Louis XIV to the French Revolution when kings ruled absolutely and citizens were without sovereignty. Discarding the traditional image of the Enlightenment as the absolute (...) enemy of absolutism, Gordon, in this sense, follows Norbert Elias and Robert Darnton who treat the Enlightenment as part of an elitist and hierarchical establishment. More specifically, as his subtitle indicates, Gordon portrays the invention of a “nonpolitical polis” (p. 6), an ideological social space where, despite political inequality, citizens could practice social equality in a hierarchical régime. The rise of this “nondemocratic egalitarian ethos” (p. 7) brought with it a new cult of sociabilité, a term invented in the eighteenth century to describe the idealization of the private sphere and the practice of social equality.The first chapter, then, ties sociability not to democracy, as in the Habermasian model, but to the absolutism that stimulated it and coexisted with it. A series of five ideal types of sociability depict how men and women, members of the bourgeoisie and the aristocracy, came together—in commerce, public welfare, scientific academies, salons, cafés, public libraries, and various other social situations not protorevolutionary in character—to create a bond among equals [End Page 279] under the ancien régime. In this framework, progress and modernity are born during the absolute monarchy where sociability suggests conviviality rather than class warfare. Every major French novel of the eighteenth century supports Gordon’s refutation of De Toqueville’s surprising statement that “noblemen and bourgeois never met except by chance in private life “in prerevolutionary France” (p. 27).In chapters two and three, Gordon examines the nature of the rules of sociability found in courtesy literature and their functioning as the imagined basis of the newly invented idealized space called société. In addition to analyzing in great detail the nature and frequency of the vocabulary invented to define and describe sociabilité, Gordon discusses sociabilité in the context of natural law theory in Hobbes, Bossuet, and among others, Pufendorf, who wanted to refute Hobbes by showing that self-interest leads humans to establish stable social relations even before government orders them to do so. Holbach surfaces here too for having amalgamated the older language of politeness and the newer language of natural law. In Holbach, as in the Encyclopédie, sociability, based on egalitarian premises of natural law, is nonetheless fully compatible with the hierarchical regime. Among other things, this shows clearly that the philosophes never preached the French Revolution. Striving to eliminate the abuses of despotism and establish equality in private life was not tantamount to working for political equality and the abolition of all rank. In this same vein, Gordon paints the apolitical essence of the private sphere and, by a rigorous study of the seventeenth-century manuals of polite living, shows convincingly (this time against Elias who saw the court as a model of refined behavior) that the salon was indeed a world unto itself, independent of preexisting social hierarchies. Rejecting Paul Hazard’s conception of absolute rupture between seventeenth-century culture and eighteenth-century thought, Gordon destroys the facile dichotomy between seventeenth-century hierarchy and eighteenth-century equality and, once again, admirably depicts the compatibility of Enlightenment and absolutism.If chapters one to three underscore a certain continuity between the seventeenth and eighteenth centuries, chapters four and five explain important changes. It is not, for example, the mere preservation of the idea of sociable communication but rather its new use that is germane in understanding the Enlightenment. Now “conversation” and “civility” no longer had meaning only for an urban elite but had in fact become ideals in all philosophical endeavors including the writing of universal history. Sociable communication had become the defining characteristic of modern nations. In the fourth chapter, by analyzing in detail the works of Jean-Baptiste Suard, Gordon demonstrates the meaning that the writing of universal history in Scotland acquired within the French... (shrink)

We give an alternative proof of the stability of separably closed fields of fixed Éršov invariant to the one given in [W]. We show that in case the Éršov invariant is finite, the theory is in fact equational. We also characterize the independence relation in those theories.

We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact e-structures. (...) In particular, we notice that a variant of the group configuration theorem holds in this context. A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed. It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits. (shrink)

This research formed phase 1 of the Economic and Social Research Council project ‘Pupils’ Approaches to Subject Option Choices’ and is a near repeat of a project carried out in the mid-1980s, thus allowing for a comparison of approaches to subject choice a decade apart, comparing the situation pre- and post-National Curriculum implementation. The simple two-part questionnaire, completed by 1600 children in 11 schools, shows the differences across time and between-school differences in subject preference, but little instability in perceptions of (...) subject importance. Some useful additional data, giving student's reasons for liking subjects and finding subjects important, were obtained from interviews in four schools which formed phase 2 of the project. Comparisons are drawn with the data collected in 1984 on a similar basis. Issues of concern are highlighted with respect to particular subjects and to students’ stated reasons for liking subjects or finding them important, with regard to how this might relate to their subsequent subject choices and career development. (shrink)

This paper argues that some educational policy slogans, particularly compound slogans, are inherently paradoxical, and that while this may have a strong motivational effect, in appealing to a wide range of ideals and aspirations, it renders both the implementation and the evaluation of certain policies problematic. The example is given of equal opportunities in relation to gender and subject choice.

We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a model-theoretic interpretation of the independence atom and characterize under which conditions we can prove a completeness result with respect to the deductive system that axiomatizes independence in team semantics and statistics.

The argument moves through three stages. In the first, the case is made for accepting ‘living is semiotic engagement’ as ‘a foundational statement for a postfoundational age’. This requires a thoroughgoing rejection of mind-body substance dualism, and a problematisation of humanism. In the second, the hazardous endeavour of applying the above perspective to social policy begins with a consideration of the sine qua non(s) underpinning such an application. These are posited as unpredictability of outcomes and blurring of the human/non-human boundary. (...) In the third stage, the case is developed for a policy orientation that is both liberal-pragmatic (with some caveats relating to ‘liberal’) and post-humanist, and the paper concludes with some speculation concerning the precise policy outcomes of such an orientation. (shrink)

Educational literature has tended to focus, explicitly and implicitly, on two kinds of task orientation: the ability either to focus on a single task, or to multi-task. A third form of orientation characterises many highly successful people. This is the ability to combine several tasks into one: to ‘kill two birds with one stone’. This skill characterises people with initiative, who exercise judgment, deliberation and creative imagination in their personal organisation. The motivation to work in this way indicates personal commitment (...) rather than mere compliance. Focusing on its development educationally implies a shift from either/or, linear, methodical, mechanical and technicist thinking to encouraging individual and collective responsibility, initiative and risk-taking, resulting in unpredictable outcomes. The emphasis on judgment renders the issues as ethical rather than narrowly instrumental. Dominant ethical approaches are, therefore, considered in relation to this in terms of its application for teaching. (shrink)

This study examines the relationship between teachers' beliefs and their practices at Key Stage 2 (ages 7-11) in relation to the use of questioning. Data were collected from interviewing and observing Key Stage 2 teachers at four schools in the West of England. A Straussian approach to grounded theory is followed broadly in order to analyse the data. In contrast to the findings of previous studies, which suggested a mismatch between teachers' beliefs and practices in that teachers, in certain (...) respects, do less than they claim, the research revealed that teachers use a variety of skills during their teaching that they may not always be aware of. It is also argued that teachers do not share researchers' language to express the way they teach. (shrink)

We prove that if T is a complete theory with weak elimination of imaginaries, then there is an explicit bijection between strict independence relations for T and strict independence relations for Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document}. We use this observation to show that if T is the theory of the Fraïssé limit of finite metric spaces with integer distances, then Teq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T^{\rm eq}}$$\end{document} has more (...) than one strict independence relation. This answers a question of Adler :1–20, 2009, Question 1.7). (shrink)

Tiebreak rules are necessary for revealing indifference in non- sequential decisions. I focus on a preference relation that satisfies Ordering and fails Independence in the following way. Lotteries a and b are indifferent but the compound lottery f, 0.5b> is strictly preferred to the compound lottery f, 0.5a>. Using tiebreak rules the following is shown here: In sequential decisions when backward induction is applied, a preference like the one just described must alter the preference relation between a (...) and b at certain choice nodes, i.e., indifference between a and b is not stable. Using this result, I answer a question posed by Rabinowicz (1997) concerning admissibility in sequential decisions when indifferent options are substituted at choice nodes. (shrink)

This paper aims to explain how semiotics and constructivism can collaborate in an educational epistemology by developing a joint approach to prescientific conceptions. Empirical data and findings of constructivist research are interpreted in the light of Peirce’s semiotics. Peirce’s semiotics is an anti-psychologistic logic and relational logic. Constructivism was traditionally developed within psychology and sociology and, therefore, some incompatibilities can be expected between these two schools. While acknowledging the differences, we explain that constructivism and semiotics share the assumption of realism (...) that knowledge can only be developed upon knowledge and, therefore, an epistemological collaboration is possible. The semiotic analysis performed confirms the constructivist results and provides a further insight into the teacher-student relation. Like the constructivist approach, Peirce’s doctrine of agapism infers that the personal dimension of teaching must not be ignored. Thus, we argue for the importance of genuine sympathy in teaching attitudes. More broadly, the article also contributes to the development of postmodern humanities. At the end of the modern age, the humanities are passing through a critical period of transformation. There is a growing interest in semiotics and semiotic philosophy in many areas of the humanities. Such a case, on which we draw, is the development of a theoretical semiotic approach to education, namely edusemiotics. (shrink)

The article gives grounds for a new paradigm of development - branding of the territory. The problem of region brand formation is actualized. The point of view of the author on the territorial branding as a technology of providing the balanced and stable socio-economic territory development in current conditions deserves particular attention. The analysis of territorial branding formation as independent marketing trend is given. The scientific interpretations of the category "territorial branding" are given. The proposition that branding is an (...) effective instrument of attracting attention to the territory is stressed. In conditions of informational and creative economy the existence of the city brand and its development strategies become the necessary factor of the effective realization of territorial potential. The conceptual framework of territorial branding and main characteristics of the utility of the territory are considered. The results of scientific research develop scientific knowledge in the field of branding territory theory, promote the development and use of intellectual and institutional resources of the territory for the growth of its marketing potential. This indicates, that the basic principles of territorial development, starting from the main concept to the specific project documents need updating, which is connected with the economic processes and also democratization and globalization processes. The cultural-economical planning gets priority, the foundation of it is the use of human and cultural capital of the city. The novelty is that material assets, traditionally considered being the basis of territorial economy development, lose their significance comparing to intangible assets, which are of various character: creative and cultural potential of the inhabitants, management professionalism, information environment saturation, the possibility to create the atmosphere of tranquility and comfort on the territory. Not the territory size and its economic base become the main success factors, but new unconventional management decisions, an energetic wish of the territory to formulate clearly its strategical interests in the country, in the region and in the world. This is the aim of the territorial branding. Currently the changing of territory development paradigm takes place. It becomes the subject of socio-economic relations, goods, intangible assets concentration. The emphasis of the development shifts towards culture, entertainment, impressions. (shrink)

Let G be a stable abelian group with regular modular generic. We show that either 1. there is a definable nongeneric K ≤ G such that G/K has definable connected component and so strongly regular generics, or 2. distinct elements of the division ring yielding the dependence relation are represented by subgroups of G × G realizing distinct strong types (when regarded as elements of G eq ). In the latter case one can choose almost 0-definable subgroups representing (...) the elements of the division ring. We find a bound $((G: G^0))$ for the size of the division ring in case G has no definable subgroup K so that G/K is infinite with definable connected component. We show in case (2) that the group G/H, where H consists of all nongeneric points of G, inherits a weakly minimal group structure from G naturally, and Th(G/H) is independent of the particular model G as long as G/H is infinite. (shrink)

The paper’s principal claim to originality lies in its deployment of Deleuze and Guattari’s concept of the ‘refrain’ in thinking the ‘resingularization’ of photography in the context of new media ecologies and the promise of what Guattari calls a ‘post-media era’. The paper itself constitutes a refrain and is structured according to the three moments of any refraining. Firstly, a refrain is a spatio-temporalization, a way of marking out space, keeping time and assembling and activating subjectivity. At its most rudimentary, (...) it is the establishment of a momentary centre, a point of order amidst chaos. We can conceive this in terms of the originary ‘cut’ of the photographic flash which – as in a familiar trope in horror films in which the flash of a camera guides the protagonist through a menacing darkness – illuminates one’s milieu, the spot on which one stands, and dispels the evils which gather on all sides. This flash is a singularity which, in rupturing darkness, does not merely constitute a representative image but is, as Guattari might say, a ‘vector of subjectivation’. Secondly, the refrain circumscribes a territory, a circle of control, ethos, interiority or home. Our media are architecture, part of the congealing and hardening of territory. Here emerges an ‘incorporeal Universe’ which signs itself ‘Photography’. We approach photographic territorialization principally in terms of genre. Photographic genres are refrains become clichés, habits, fictions which uncritically sustain and abet the ravages of capitalistic subjectivity. Adhering, photographically, to these affective algorithms – creatively reacting in the belief that There Is No Alternative – is to generatively maintain the existence of a virtually stable territory. It is this territory that, we insist, requires estrangement through the amplification of its moments of uncertainty. The third moment of the refrain is precisely the exacerbation of its instability, its transformation into a ‘music’ which is the cracking open of the territory to the world and its opening out onto futurity and alterity. We conceive this in two ways. On the one hand, the opening of the photographic refrain can be understood in terms of the ontology of mediation. Rather than a freezing of the moment, the photographic image is in and of the middle, medial – that is, it constitutes an event of interruptive time, the construction of an interval which is excessive and untimely. Here, we heed recent calls for a new ethics of photographic practice which understands and takes responsibility for the process of mediation ‘from within the process itself’. On the other hand, the opening of the photographic refrain can be understood in connection with the subjective pluralism which is the excess of the social. We are plural, polyphonic subjects, comprising affective communities which exist in relation to a ‘constellation of Universes’, at the intersection of refrains which variously harness anti-chaotic forces and can be resingularized and opened onto the forces of the future. Along lines intimated by Guattari, we commend the collective reappropriation and resingularization of photography in order to escape its impasse, to reflexively trigger ‘an existential agglomeration’. Mediation itself offers the promise of a ‘post-media era’ in which we liberate the creativity and virtuality of media in order to ‘bifurcate existence’, realizing the possibility of new constellations of Universes and an autopoiesis of subjectivity. Tapping into such excess requires a pedagogy of excess, too. For us, to respond ethically to the new powers of mediation means respecifying photography as a collective endeavour, beyond the principles of ‘self expression’ and ‘independence’ which have long dominated photography education. It also means going beyond the conventions of genre and ‘socially-engaged’ practice, not simply through the usual judgement and denunciation of territory but through its falsification. As we see it, photography’s ‘fabulatory function’ is to both make perceptible and betray the ‘working forces’ of territorial refrains, to both activate and ‘fail to satisfy’ them. Indeed, it is in this sense that photography might become a transversal tool with which to think the artistic and social simultaneously. (shrink)

A century after the advent of quantum mechanics and general relativity, both theories enjoy incredible empirical success, constituting the cornerstones of modern physics. Yet, paradoxically, they suffer from deep-rooted, so-far intractable, conflicts. Motivations for violations of the notion of relativistic locality include the Bell’s inequalities for hidden variable theories, the cosmological horizon problem, and Lorentz-violating approaches to quantum geometrodynamics, such as Horava–Lifshitz gravity. Here, we explore a recent proposal for a “real ensemble” non-local description of quantum mechanics, in which “particles” (...) can copy each others’ observable values AND phases, independent of their spatial separation. We first specify the exact theory, ensuring that it is consistent and has quantum mechanics as a fixed point, where all particles with the same values for a given observable have the same phases. We then study the stability of this fixed point numerically, and analytically, for simple models. We provide evidence that most systems are locally stable to small deviations from quantum mechanics, and furthermore, the phase variance per value of the observable, as well as systematic deviations from quantum mechanics, decay as \ time)\, where \. Interestingly, this convergence is controlled by the absolute value of energy, suggesting a possible connection to gravitational physics. Finally, we discuss different issues related to this theory, as well as potential novel applications for the spectrum of primordial cosmological perturbations and the cosmological constant problem. (shrink)

The study is relevant as long as it highlights the existing approaches to political-administrative relations in the incipient democratic state, focusing on the defining aspects of the main European models. Analysis of literature. The article has made use of the work of foreign researchers such as Max Weber, Woodrow Wilson, Frank Johnson Goodnow, Luther Gulick, Kenneth J. Meier, Laurence J. O'Thole Jr., Christopher Pollitt, Geert Bouckaert, James H. Svara, Jon Pierre, Carl Friedrich, Fred Kramer, and the natives such as V. (...) Juc, V. Saca, G. Rusnac, A. Zavtur, A. Popovici, C. Solomon, P. Fruntasu, V. Popa, V. Mosneaga and I. Bucataru. The aim of the article is to determine the type of optimal political and administrative relations to ensure open and responsible governance in countries with early democratic regimes. Research objectives are reduced to the study of the various models of public administration that have been going on in time, in order to determine the particularities that are compatible with the specifics of the countries with a transition democracy. Research Methodology. The study is based on comparative analysis and inductive and deductive reasoning. The result of the study. At present, the theories and models used by researchers are limited to the two extremes, namely the separation of the politicians of the administrators, on the one hand, and the argumentation of the complementarity between politics and administration, on the other. Both theoretical models have been implemented in practice through three public administration systems: continental, mixed and British. Until now, there are various debates about the viability of the two models in academic environment, and there is no real possibility of achieving a complete separation of the roles and goals of politicians and bureaucrats, and that the supreme power in a state is politics, irrespective of its designation. As regards the political-administrative relationship in the states with an incipient democracy, it is observed over the decades of independence, the use in the relations of the authoritarian methods with a democratic decoration, aimed at satisfying the noble, or rather subject to, narrow interests by the ruling and opposition forces, which absolutely did not take the public interest into account. Conclusions. In the desperate attempt to find a genuine way to approach political-administrative relations in countries with early democracies, we find it stupors that it is hard to suggest the implementation of a pure model, but the optimal model implies the existence of a freely chosen political power and a an autonomous, efficient and stable administrative sector that corresponds to the orders of that power. (shrink)

Elgin has presented an extensive defence of reflective equilibrium embedded in an epistemology which focuses on objectual understanding rather than ordinary propositional knowledge. This paper has two goals: to suggest an account of reflective equilibrium which is sympathetic to Elgin’s but includes a range of further developments, and to analyse its role in an account of understanding. We first address the structure of reflective equilibrium as a target state and argue that reflective equilibrium requires more than an equilibrium in the (...) sense of a coherent position. On the one hand, the position also needs to be stable between a ‘conservative’ pull of input commitments and a ‘progressive’ pull of epistemic goals; on the other hand, reflective equilibrium requires that enough of the resulting commitments have some credibility independent of the coherence of the position. We then turn to the dynamics of reflective equilibrium, the process of mutual adjustment of commitments and theories. Here, the most pressing internal challenges for defenders of reflective equilibrium arise: to characterize this process more exactly and to explain its status in relation to reflective equilibrium as a target state. Finally, we investigate the role of reflective equilibrium in Elgin’s account of understanding and argue that objectual understanding cannot be explained in terms of reflective equilibrium alone. An epistemic agent who understands a subject matter by means of a theory also needs to be able to use this theory and the theory needs to meet some external rightness condition. (shrink)

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instance, a full appreciation of Axelrod's The Evolution of Cooperation requires that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questions we re-examine the very foundations of the evolutionary model. The results of this paper can be analytically separated into three (...) parts. The first part is conceptual: it identifies the evolutionary model's assumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stability identified in the first part, and demonstrates in which games these kinds of stability can (and cannot) be attained. The third and final part is applied: it relates the general findings (which are independent of the specific payoffs of any particular evolutionary game) to the issue of the evolutionary stability of cooperation. Results on cooperation appear throughout the paper as they both exemplify and motivate the general results. These results essentially explain when cooperation is and is not stable, and why, thus shedding new light on the meaning and applicability of Axelrod's widely known claims. (shrink)

Following Kant, Frege took the idea that there is such a thing as bona fide a priori knowledge of a large range of necessary propositions for granted. In particular he assumed that such is the character of our knowledge of basic logic and arithmetic. This view is no longer orthodoxy. The idea that pure (for Frege, logical) intellection can provide for substantial knowledge of necessary features of the world is widely regarded with suspicion. However it is fair to say that (...) most recent scepticism about it has been driven either by abstract background theoretical commitments—for instance, by a thoroughgoing empiricism, as in Mill and Quine, or by epistemological externalism1—or by the conviction that the concept of a priori justification allows of no stable, theoretically interesting characterisation.2 The present discussion focuses on the example of elementary arithmetic to develop and explore a different, relatively neglected and, it may be suggested, more fundamental kind of sceptical challenge, one prefigured in the writings on mathematics of the later Wittgenstein but independent of the discussion of following a rule to which his generally deflationary or conventionalist cast of thinking about mathematical knowledge is, after Kripkenstein,3 nowadays usually attributed. Elementary arithmetical truths are normally taken to be justifiable a priori if any truths are. They are also normally taken to be both necessary and substantial—essentially applicable to our dealings with the world and empirically predictive, yet good for counterfactual reasoning about however far-fetched and exotic scenarios. Yet, I will argue, scrutiny of the kind of methods—simple informal cognitive routines involving counting and pictures—whereby such judgements are initially apt to win our confidence serves to make it puzzling how they can justify what they are supposed to at all: how such procedures can merit either the very high levels of confidence we standardly place in the judgements they lead to, or the modal (counterfactual) significance we standardly attach to those judgements. The present discussion elaborates these apparent shortfalls (§§2–4) and reviews four proposals (§§5–8) for redressing them, arguing that each is ineffective. The sceptical challenge accordingly stands unanswered. §9 elaborates its relation to one strand in the Remarks on the Foundations of Mathematics. §10 summarises the resulting dialectical position. The upshot, I believe, is a deepened understanding of an important aspect of Wittgenstein’s later philosophy and a major intellectual challenge to those—possibly still a majority—who incline to side with Frege’s view of the epistemological status of arithmetic. (shrink)

We address the question whether there is an explanation for the fact that as Fodor put it the micro-level “converges on stable macro-level properties”, and whether there are lessons from this explanation for other issues in the vicinity. We argue that stability in large systems can be understood in terms of statistical limit theorems. In the thermodynamic limit of infinite system size N → ∞ systems will have strictly stable macroscopic properties in the sense that transitions between different (...) macroscopic phases of matter (if there are any) will not occur in finite time. Indeed stability in this sense is a consequence of the absence of fluctuations, as (large) fluctuations would be required to induce such macroscopic transformations. These properties can be understood in terms of coarse-grained descriptions, and the statistical limit theorems for independent or weakly dependent random variable describing the behaviour averages and the statistics of fluctuations in the large system limit. We argue that RNG analyses applied to off-critical systems can provide a rationalization for the applicability of these limit theorems. Furthermore we discuss some related issues as, for example, the role of the infinite-system idealization. (shrink)

In this paper we present stable and unstable versions of several well-known relations from mereotopology: part-of, overlap, underlap and contact. An intuitive semantics is given for the stable and unstable relations, describing them as dynamic counterparts of the base mereotopo-logical relations. Stable relations are described as ones that always hold, while unstable relations hold sometimes. A set of first-order sentences is provided to serve as axioms for the stable and unstable relations, and representation theory is developed (...) in similar fashion to Stone’s representation theory for Boolean algebras and distributive lattices. Then we present some results about the first-order predicate logic of these relations and about its quantifier-free fragment. Completeness theorems for these logics are proved, the full first-order theory is proved to be hereditary undecidable and the satisfiability problem of the quantifier-free fragment is proved to be NP-complete. (shrink)