A large homogeneous model M is strongly minimal, if any definable subset is either bounded or has bounded complement. In this case is a pregeometry, where bcl denotes the bounded closure operation. In this paper, we show that if M is a large homogeneous strongly minimal structure and is non-trivial and locally modular, then M interprets a group. In addition, we give a description of such groups.

Assume G is a superstable locally modular group. We describe for any countable model M of Th(G) the quotient group G(M) / Gm(M). Here Gm is the modular part of G. Also, under some additional assumptions we describe G(M) / Gm(M) relative to G⁻(M). We prove Vaught's Conjecture for Th(G) relative to Gm and a finite set provided that ℳ(G) = 1 and the ring of pseudoendomorphisms of G is finite.

La sapienza di partire da sè è una via che si sottrae alle molte contrapposizioni che sono iscritte nel simbolico dominante: quella tra soggettivo e oggettivo, tra individuo e comunità e tra locale e generale: apre un'altra strada.

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its precise conceptual-mathematical formulation as “modular localization” within the setting of local operator algebras also suggests novel ways of looking at general (non-integrable) QFTs which are not based on quantizing classical field theories.Conformal QFT, which is known to admit no particle interpretation, suggest the presence of (...) a “partial” integrability, referred to as “conformal integrability”. This manifests itself in a “braid-permutation” group structure which contains in particular informations about the anomalous dimensional spectrum. For chiral conformal models this reduces to the braid group as it is represented in Hecke- or Birman-Wenzl-algebras associated to chiral models.Another application of modular localization mentioned in this work is an alternative to the BRST formulation of gauge theories in terms of stringlike vectorpotentials within a Hilbert space setting. (shrink)

In recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or in the $\omega$-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity. The proof necessitated an extension of the model-theoretic framework to (...) include almost hyperimaginaries, and the study of polygroups. (shrink)

We study hyperdefinable groups, the most general kind of groups interpretable in a simple theory. After developing their basic theory, we prove the appropriate versions of Hrushovski's group quotient theorem and the Weil–Hrushovski group chunk theorem. We also study locally modular hyperdefinable groups and prove that they are bounded-by-Abelian-by-bounded. Finally, we analyze hyperdefinable groups in supersimple theories.

In a recent communication an uncountably categorical group has been constructed that has a non-locally-modular geometry and does not allow the interpretation of a field. We consider a system Δ of elementary axioms fulfilled by some special subgroups of the above group. We show that Δ is complete and stable, but not superstable. It is not even a R-group in the sense discussed by Wagner.

In this paper we deal with the model theory of differentially closed fields of characteristic zero with finitely many commuting derivations. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types which are orthogonal to fields. Then we classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are (...) nonorthogonal to fields. The last parts consist of an analaysis of the quotients of the heat variety. We show that the generic type of such a quotient is locally modular. Finally, we answer a question of Phylliss Cassidy about the existence of certain Jordan-Holder type series in the negative. (shrink)

Members of a human group are bound with one another by multiple flows of information. (Here we use “information” in a broad sense that includes not only the content of people’s knowledge, but also that of their beliefs, assumptions, fictions, rules, norms, skills, maps, images, and so on.) This information is materially realized in the mental representations of the people, and in their public productions, that is, their cognitively guided behaviors and the enduring material traces of these behaviors. Mentally (...) represented information is transmitted from individuals to individuals through public productions. Public representations such as speech, gestures, writing, or pictures are a special type of public productions, the function of which is to communicate a content. Public representations play a major role in information transmission. Much information, however, is communicated implicitly, that is, without being publicly represented. Information can also be transmitted without being properly speaking communicated, not even implicitly, as when one individual acquires a skill by observing and imitating the behavior of others. Most information transmitted among humans is about local and transient circumstances, and is not transmitted beyond these. Some information of more general relevance, however, is repeatedly transmitted, and propagates throughout the group. Talk of “culture” (whatever the preferred definition or theory of culture) is about this widely distributed information and about its material realizations inside people’s mind and in their common environment (see Sperber 1996). One can study cultural phenomena in two main ways. One can interpret them, that is, try and make their contents intelligible to people of another culture, or more intelligible to members of the culture in which these phenomena occurs, as do anthropologists and historians. One may also try and explain causally how these cultural phenomena emerge, stabilize and evolve.. (shrink)

We study the infinitely definable subgroups of the additive group in a separably closed field of finite positive imperfection degree. We give some constructions of families of such subgroups which confirm the diversity and the richness of this class of groups. We show in particular that there exists a locally modular minimal subgroup such that the division ring of its quasi-endomorphisms is not a fraction field of the ring of its definable endomorphisms, and that in contrast there (...) exist 20 pairwise orthogonal locally modular minimal subgroups whose induced structure is exactly that of an-vector space. We also show that there exist infinitely many pairwise orthogonal subgroups of infinite U-rank. Furthermore, these constructions are carried out in the additive group considered as a module over its ring of definable endomorphisms. (shrink)

We reconstruct the group action in the group configuration theorem. We apply it to show that in an ω-categorical theory a finitely based pseudolinear regular type is locally modular, and the geometry associated to a finitely based locally modular regular type is projective geometry over a finite field.

We will study some aspects of the local structure of models of certain C-minimal theories. We will prove (theorem 19) that, in a sufficiently saturated C-minimal structure in which the algebraic closure has the exchange property and which is locally modular, we can construct an infinite type-definable group around any non trivial point (a term to be defined later). On va étudier ici certains aspects de la structure locale des modèles de certaines théories C-minimales. On va prouver (...) (théorème 19) que, dans une structure C-minimale suffisamment saturée, localement modulaire et dans laquelle la clôture algébrique permet de définir une notion de dimension, on peut construire un groupe type-définissable infini autour de tout point non trivial (terme à définir par la suite). (shrink)

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the (...) game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory. (shrink)

We show that if M is a strongly minimal large homogeneous structure in a countable similarity type and the pregeometry of M is locally modular but not modular, then the pregeometry is affine over a division ring.

There is a distinction between locality and modularity. These two terms have often been used interchangeably in the target article and commentary. Using this distinction we argue in favor of a modularity. In addition we also argue that both PDP-type networks and box-and-arrow models have their own strengths and pitfalls.

Let $M$ be a saturated model of a superstable theory and let $G = \operatorname{Aut}(M)$. We study subgroups $H$ of $G$ which contain $G_{(A)}, A$ the algebraic closure of a finite set, generalizing results of Lascar [L] as well as giving an alternative characterization of the simple superstable theories of [P]. We also make some observations about good, locally modular regular types $p$ in the context of $p$-simple types.

For a locally compact group G, we show that it is possible to present the class of continuous unitary representations of G as an elementary class of metric structures, in the sense of continuous logic. More precisely, we show how nondegenerate ∗-representations of a general ∗-algebra A (with some mild assumptions) can be viewed as an elementary class, in a many-sorted language, and use the correspondence between continuous unitary representations of G and nondegenerate ∗-representations of L1(G). We relate (...) the notion of ultraproduct of logical structures, under this presentation, with other notions of ultraproduct of representations appearing in the literature, and we characterize property (T) for G in terms of the definability of the sets of fixed points of L1 functions on G. (shrink)

Deep-rooted political turbulence, along with the present hybrid regime, have resulted in an undesirable social, economic and political milieu in Serbia. Such an atmosphere is a fertile ground for a grey economy, corruption, nepotism and restrictions to media freedoms. These?unconventional? means of social functioning, have caused a decline in trust towards state institutions and proportionally, increase of citizen participation in non-institutional models of engagement. The aim of this paper is to analyse one such model of non-institutional engagement: the local activist (...) group Za nas Kej, operating in the area Savski blokovi in New Belgrade. The authors analysed local residents? perception of the activist group Za nas Kej in comparison to the group?s narratives and actions. By using a grounded theory approach authors explained the role of groups such as Za Nas Kej in the development of participatory and deliberative democracy within the local community. Our data indicates that Za nas kej, despite its local character, does not have a strong foothold in the community, and thus receives only passive support. Citizens perceive Za nas kej as mediator between local institutions and residents of the Sava apartment blocks. Despite the failure to mobilise a wider group of citizens for their cause, this activist group continues to be a relevant actor within the local community. (shrink)

We prove the following instance of a conjecture stated in [P. E. Eleftheriou and Y. Peterzil, Definable quotients of locally definable groups, Selecta Math. 18 885–903]. Let [Formula: see text] be an abelian semialgebraic group over a real closed field [Formula: see text] and let [Formula: see text] be a semialgebraic subset of [Formula: see text]. Then the group generated by [Formula: see text] contains a generic set and, if connected, it is divisible. More generally, the same (...) result holds when [Formula: see text] is definable in any o-minimal expansion of [Formula: see text] which is elementarily equivalent to [Formula: see text]. We observe that the above statement is equivalent to saying: there exists an [Formula: see text] such that [Formula: see text] is an approximate subgroup of [Formula: see text]. (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)

T is stable. We define the notion of meager regular type and prove that a meager regular type is locally modular. Assuming I < 2o and G is a definable abelian group with locally modular regular generics, we prove a counterpart of Saffe's conjecture. Using these results, for superstable T we prove the conjecture of vanishing multiplicities. Also, as a further application, in some additional cases we prove a conjecture regarding topological stability of pseudo-types over (...) Q. (shrink)

Certain basic concepts of geometrical stability theory are generalized to a class of closure operators containing algebraic closure. A specific case of a generalized closure operator is developed which is relevant to Vaught's conjecture. As an application of the methods, we prove THEOREM A. Let G be a superstable group of U-rank ω such that the generics of G are locally modular and Th(G) has few countable models. Let G - be the group of nongeneric elements (...) of G, G + = G o + G - . Let Π= {q ∈ S( $\emptyset$ ): U(q) $A \subset M$ such that M is almost atomic over A ∪ (G + ∩ M) $\cup \bigcup_{p\in \Pi}$ p(M). (shrink)

We prove here:Theorem. LetT be a countable complete superstable non ω-stable theory with fewer than continuum many countable models. Then there is a definable groupG with locally modular regular generics, such thatG is not connected-by-finite and any type inG eq orthogonal to the generics has Morley rank.Corollary. LetT be a countable complete superstable theory in which no infinite group is definable. ThenT has either at most countably many, or exactly continuum many countable models, up to isomorphism.

We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

In this note we study some local properties ofω-stable groups of finite Morley rank.

The notion of modularity, introduced by Noam Chomsky and developed with special emphasis on perceptual and linguistic processes by Jerry Fodor in his important book The Modularity of Mind, has provided a significant stimulus to research in cognitive science. This book presents essays in which a diverse group of philosophers, linguists, psycholinguists, and neuroscientists - including both proponents and critics of the modularity hypothesis - address general questions and specific problems related to modularity. Jay L. Garfield is Associate Professor (...) of Philosophy in the School of Communications and Cognitive Science at Hampshire College. (shrink)

It is unreasonable to assume that our pre-scientific emotion vocabulary embodies all and only those distinctions required for a scientific psychology of emotion. The psychoevolutionary approach to emotion yields an alternative classification of certain emotion phenomena. The new categories are based on a set of evolved adaptive responses, or affect-programs, which are found in all cultures. The triggering of these responses involves a modular system of stimulus appraisal, whose evoluations may conflict with those of higher-level cognitive processes. Whilst the (...) structure of the adaptive responses is innate, the contents of the system which triggers them are largely learnt. The circuits subserving the adaptive responses are probably located in the limbic system. This theory of emotion is directly applicable only to a small sub-domain of the traditional realm of emotion. It can be used, however, to explain the grouping of various other phenomena under the heading of emotion, and to explain various characteristic failings of the pre-scientific conception of emotion. (shrink)

Structuralism can be defined as an important concept of using “units” as elements of form and space-giving, where the whole form is made not only up of a “texture”, a certain flexible grid, or an algorithm of shape-giving, but it depends also on the relationships created and how people use it. The hypothesis of this study is that “Modular Construction” can also have an aesthetically pleasing outlook and that modular housing can definitely have increasing importance in the future. (...) Modular housing due to its cheap, and manufactural way of construction can be replicable in various locations. Structuralism and Modular Construction have been at the core of the Modernist movement. Although postmodernism marked the decline of modular construction adopting methods known for a more close sense of place, vernacular, and locality, which differs from the ubiquitous model of modernism, it is the universality of space and habitation seen since the times of Hippodamus Grid, Japanese Tattami systems, and rational universal space in housing known in Europe that make grid and modular design an excellent system in obtaining, rationality, functionality, flexibility, and energy efficiency, including quick construction and possibility for replication. In this regard, modular construction has a future, especially in times of crisis and economic instability. (shrink)

It is unreasonable to assume that our pre-scientific emotion vocabulary embodies all and only those distinctions required for a scientific psychology of emotion. The psychoevolutionary approach to emotion yields an alternative classification of certain emotion phenomena. The new categories are based on a set of evolved adaptive responses, or affect-programs, which are found in all cultures. The triggering of these responses involves a modular system of stimulus appraisal, whose evoluations may conflict with those of higher-level cognitive processes. Whilst the (...) structure of the adaptive responses is innate, the contents of the system which triggers them are largely learnt. The circuits subserving the adaptive responses are probably located in the limbic system. This theory of emotion is directly applicable only to a small sub-domain of the traditional realm of emotion. It can be used, however, to explain the grouping of various other phenomena under the heading of emotion, and to explain various characteristic failings of the pre-scientific conception of emotion. (shrink)

Given a Polish groupG, let$E(G)$be the right coset equivalence relation$G^{\omega }/c(G)$, where$c(G)$is the group of all convergent sequences inG. The connected component of the identity of a Polish groupGis denoted by$G_0$.Let$G,H$be locally compact abelian Polish groups. If$E(G)\leq _B E(H)$, then there is a continuous homomorphism$S:G_0\rightarrow H_0$such that$\ker (S)$is non-archimedean. The converse is also true whenGis connected and compact.For$n\in {\mathbb {N}}^+$, the partially ordered set$P(\omega )/\mbox {Fin}$can be embedded into Borel equivalence relations between$E({\mathbb {R}}^n)$and$E({\mathbb {T}}^n)$.

The claim that the human cognitive system tends to allocate resources to the processing of available inputs according to their expected relevance is at the basis of relevance theory. The main thesis of this chapter is that this allocation can be achieved without computing expected relevance. When an input meets the input condition of a given modular procedure, it gives this procedure some initial level of activation. Input-activated procedures are in competition for the energy resources that would allow them (...) to follow their full course. What determines which of the procedures in competition get sufficient resources to trigger their full operation is the dynamics of their activation. This dynamics depend both on the prior degree of mobilisation of a modular procedure and on the activation that propagates from other active modules. It is quite conceivable also that the mobilisation of some procedures has inhibitory effects on some others. The relevance-theoretic claim is that, at every instant, this dynamics of activation provides rough physiological indicators of expected relevance. The flow of energy in the system is locally regulated by these indicators. As a result, those input-procedure combinations that have the greatest expected relevance are the more likely ones to receive sufficient energy to follow their course. (shrink)

Although disoriented young children reorient themselves in relation to the shape of the surrounding surface layout, cognitive accounts of this ability vary. The present paper tests three theories of reorientation: a snapshot theory based on visual image-matching computations, an adaptive combination theory proposing that diverse environmental cues to orientation are weighted according to their experienced reliability, and a modular theory centering on encapsulated computations of the shape of the extended surface layout. Seven experiments test these theories by manipulating four (...) properties of objects placed within a cylindrical space: their size, motion, dimensionality, and distance from the space’s borders. Their findings support the modular theory and suggest that disoriented search behavior centers on two processes: a reorientation process based on the geometry of the 3D surface layout, and a beacon-guidance process based on the local features of objects and surface markings. Ó 2010 Elsevier Inc. All rights reserved. (shrink)

Three experiments investigated the modularity of harmonic expectations that are based on cultural schemata despite the availability of more predictive veridical information. Participants were presented with prime–target chord pairs and made an intonation judgment about each target. Schematic expectation was manipulated by the combination of prime and target, with some transitions being schematically more probable than others. Veridical information in the form of prime–target previews, local transition probabilities, or valid versus invalid previews was also provided. Processing was facilitated when a (...) schematically probable target chord followed the prime. Furthermore, this effect was independent of all manipulations of veridical expectation. A solution to L. B. Meyer's (1967b) query "On Rehearing Music" is suggested, in which schematic knowledge contributes to harmonic expectation in a modular manner regardless of whether any veridical knowledge exists. (shrink)

Over the past four decades the world has seen a 'Green awakening'. Green parties have been elected to parliaments and councils all over the world, and in many cases have played a part in national and local government. A common set of Green priorities has been promoted by Green internationalisation and these parties are playing an increasing role at all levels of political decision-making. Will the Green awakening continue or will Greens be corrupted by power? What impact has Green politics (...) had? Will Green thinking be able to compete with other ideologies in coping with the problems of the 21st century? Green Parties, Green Future analyses these issues on the basis of the experience of Green parties from all parts of the world. Per Gahrton, a sociologist and veteran of Green politics, provides the whole story of the expansion and development of the Greens worldwide, from local environmental groups to national and global decision-makers. This is essential reading for anyone who is or wants to be involved in a political movement that is challenging the more traditional parties for a progressive future. (shrink)

What follows is a discussion of three sets of experimental results that deal with various aspects of universal biological understanding among American and Maya children and adults. The first set of experiments shows that by the age of four-to-five years urban American and Yukatek Maya children employ a concept of innate species potential, or underlying essence, as an inferential framework for understanding the affiliation of an organism to a biological species, and for projecting known and unknown biological properties to organisms (...) in the face of uncertainty. The second set of experiments shows that the youngest Maya children do not have an anthropocentric understanding of the biological world. Children do not initially need to reason about non-human living kinds by analogy to human kinds. The third set of results show that the same taxonomic rank is cognitively preferred for biological induction in two diverse populations: people raised in the Mid-western USA and Itza' Maya of the Lowland Meso-american rainforest. This is the generic species  the level of oak and robin. These findings cannot be explained by domain-general models of similarity because such models cannot account for why both cultures prefer species-like groups in making inferences about the biological world, although Americans have relatively little actual knowledge or experience at this level. The implication from these experiments is that folk biology may well represent an evolutionary design: universal taxonomic structures, centred on essence-based generic species, are arguably routine products of our ‘habits of mind,' which may be in part naturally selected to grasp relevant and recurrent ‘habits of the world.' The science of biology is built upon these domain-specific cognitive universals: folk biology sets initial cognitive constraints on the development of any possible macro-biological theory, including the initial development of evolutionary theory. Nevertheless, the conditions of relevance under which science operates diverge from those pertinent to folk biology. For natural science, the motivating idea is to understand nature as it is ‘in itself,' independently of the human observer. From this standpoint, the species-concept, like taxonomy and teleology, may arguably be allowed to survive in science as a regulative principle that enables the mind to readily establish stable contact with the surrounding environment, rather than as an epistemic concept that guides the search for truth. (shrink)

Currently, there is widespread skepticism that higher cognitive processes, given their apparent flexibility and globality, could be carried out by specialized computational devices, or modules. This skepticism is largely due to Fodor's influential definition of modularity. From the rather flexible catalogue of possible modular features that Fodor originally proposed has emerged a widely held notion of modules as rigid, informationally encapsulated devices that accept highly local inputs and whose operations are insensitive to context. It is a mistake, however, to (...) equate such features with computational devices in general and therefore to assume, as Fodor does, that higher cognitive processes must be non‐computational. Of the many possible non‐Fodorean architectures, one is explored here that offers possible solutions to computational problems faced by conventional modular systems: an ‘enzymatic’ architecture. Enzymes are computational devices that use lock‐and‐key template matching to identify relevant information (substrates), which is then operated upon and returned to a common pool for possible processing by other devices. Highly specialized enzymes can operate together in a common pool of information that is not pre‐sorted by information type. Moreover, enzymes can use molecular ‘tags’ to regulate the operations of other devices and to change how particular substrates are construed and operated upon, allowing for highly interactive, context‐specific processing. This model shows how specialized, modular processing can occur in an open system, and suggests that skepticism about modularity may largely be due to failure to consider alternatives to the standard model. (shrink)