We study the class of ω-categorical structures with n-degenerate algebraic closure for some n ε ω, which includes ω-categorical structures with distributive lattice of algebraically closed subsets , and in particular those with degenerate algebraic closure. We focus on the models of ω-categorical universal theories, absolutely ubiquitous structures, and ω-categorical structures generated by an indiscernible set. The assumption of n-degeneracy implies total categoricity for the first class, stability for the second, and ω-stability for the third.

The weak non-finite cover property (wnfcp) was introduced in [1] in connection with "axiomatizability" of lovely pairs of models of a simple theory. We find a combinatorial condition on a simple theory equivalent to the wnfcp, yielding a direct proof that the non-finite cover property implies the wnfcp, and that the wnfcp is preserved under reducts. We also study the question whether the wnfcp is preserved when passing from a simple theory T to the theory TP of lovely pairs of (...) models of T (true in the stable case). While the question remains open, we show, among other things, that if (for a T with the wnfcp) TP is low, then TP has the wnfcp. To study this question, we describe "double lovely pairs", and, along the way, we develop the notion of a "lovely n-tuple" of models of a simple theory, which is an analogue of the notion of a beautiful tuple of models of stable theories [2]. (shrink)

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T . We show that the theory T* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T* coincides with the theory of infinite dimensional pairs, which was used in 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T* for the same purpose. In particular, we obtain a characterization of linearity (...) for SU-rank 1 structures by giving several equivalent conditions on T*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures. (shrink)

We continue the study of the connection between the “geometric” properties of SU -rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU-rank of the theory of generic pairs of models of an SU -rank 1 theory T can only take values 1 , 2 or ω, generalizing the corresponding results for a strongly minimal T in [3]. We also use pairs to derive the implication from pseudolinearity to (...) linearity for ω -categorical SU -rank 1 structures, established in [7], from the conjecture that an ω -categorical supersimple theory has finite SU -rank, and find a condition on generic pairs, equivalent to pseudolinearity in the general case. (shrink)

We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil–Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair.

Given a lovely pair P ≺ M of models of a simple theory T, we study the structure whose universe is P and whose relations are the traces on P of definable (in ℒ with parameters from M) sets in M. We give a necessary and sufficient condition on T (which we call weak lowness) for this structure to have quantifier-elimination. We give an example of a non-weakly-low simple theory.

We study expansions of an algebraically closed field K or a real closed field R with a linearly independent subgroup G of the multiplicative group of the field or the unit circle group \\), satisfying a density/codensity condition. Since the set G is neither algebraically closed nor algebraically independent, the expansion can be viewed as “intermediate” between the two other types of dense/codense expansions of geometric theories: lovely pairs and H-structures. We show that in both the algebraically closed field and (...) real closed field cases, the resulting theory is near model complete and the expansion preserves many nice model theoretic conditions related to the complexity of definable sets such as stability and NIP. (shrink)

We study definable groups in dense/codense expansions of geometric theories with a new predicate P such as lovely pairs and expansions of fields by groups with the Mann property. We show that in such expansions, large definable subgroups of groups definable in the original language \ are also \-definable, and definably amenable \-definable groups remain amenable in the expansion. We also show that if the underlying geometric theory is NIP, and G is a group definable in a model of T, (...) then the connected component \ of G in the expansion agrees with the connected component \ in the original language. We prove similar preservation results for \^n\), the P-part of G in a lovely pair, and for subgroups of G in pairs where R is a real closed field and G is a subgroup of \ or the unit circle \\) with the Mann property. (shrink)

We study the class of weakly locally modular geometric theories introduced in [4], a common generalization of the classes of linear SU-rank 1 and linear o-minimal theories. We find new conditions equivalent to weak local modularity: "weak one-basedness", absence of type definable "almost quasidesigns", and "generic linearity". Among other things, we show that weak one-basedness is closed under reducts. We also show that the lovely pair expansion of a non-trivial weakly one-based ω-categorical geometric theory interprets an infinite vector space over (...) a finite field. (shrink)

We study the theory of the structure induced by parameter free formulas on a “dense” algebraically independent subset of a model of a geometric theory T. We show that while being a trivial geometric theory, inherits most of the model theoretic complexity of T related to stability, simplicity, rosiness, the NIP and the NTP2. In particular, we show that T is strongly minimal, supersimple of SU‐rank 1, has the NIP or the NTP2 exactly when has these properties. We show that (...) if T is superrosy of thorn rank 1, then so is, and that the converse holds if T satisfies acl = dcl. (shrink)

We introduce the notion of a lovely pair of models of a simple theory T, generalizing Poizat's “belles paires” of models of a stable theory and the third author's “generic pairs” of models of an SU-rank 1 theory. We characterize when a saturated model of the theory TP of lovely pairs is a lovely pair , finding an analog of the nonfinite cover property for simple theories. We show that, under these hypotheses, TP is also simple, and we study forking (...) and canonical bases in TP. We also prove that assuming only that T is low, the existentially universal models of the universal part of a natural expansion TP+ of TP, are lovely pairs, and “simple Robinson universal domains”. (shrink)

Based on the work done in [][] in the o‐minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking‐independent elements that is dense inside a partial type, which we call H‐structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again H‐structures. We prove that under these assumptions the expansion is supersimple and (...) characterize forking and canonical bases of types in the expansion. We also analyze the effect these expansions have on one‐basedness and CM‐triviality. In the one‐based case, when T has SU‐rank and the SU‐rank is continuous, we take to be the type of elements of SU‐rank and we describe a natural “geometry of generics modulo H” associated with such expansions and show it is modular. (shrink)

The problem, of man falls into a category of problems of human knowledge that are both ‘eternal’ and ever new. Countless legends, myths, philosophical systems, religious doctrines, scientific conceptions and fantastic visions have been the fruit of man's ungovernable desire to know himself, to know his essence, his purpose in the world, his fate, his future. Not to mention the ingenious hypotheses and Utopian fantasms, scientific truths and galling mistakes, bold projects and cowardly superstitions handed on by human civilization in (...) its Indefatigable search for the ‘magic crystal’ which would at last reveal man's true nature. All periods have made their contribution In this everlasting quest and all have relied on the few parcels of truth gleaned by humanity at earlier stages of development. Our times, the most dramatic and revolutionary of all, are by no means an exception and can be distinguished from the rest only by the exceptional acuity and urgency of the problem. (shrink)

'This book is a masterpiece of theoretical thought. It anticipates the actual achievements of much of what we now call sociolinguistics.

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

Purpose. The knowledge influence analysis on the formation process of new anthropological images of man in the contexts of scientific achievements and innovative technologies is the basis of this study. It involves the solution of the following tasks: 1) explication of the ontological content of knowledge in the anthropo-cultural senses of the epoch; 2) analysis of the knowledge influence on the process of forming a new type of man; 3) characteristics of the modern anthropological situation in the context of digital (...) culture; 4) substantiation of interrelation of phatic communication with post-truth society in the dimensions of anthropo-social transformations of the present. Theoretical basis. Ontological content of knowledge determines the anthropo-cultural context of the epoch by forming a system of intellectual, value, social meanings of human life. The assertion of new anthropological types of man is caused by the changes in social and cultural space in the context of the growing influence of achievements in scientific knowledge and technology. Digital revolution as the process of expanding the possibilities of informational-digital reality, the substitution of knowledge for information gives rise to Homo digitalis – the digital man. He focuses on phatic communication, which in its intellectual meaninglessness is commensurate with the anthropological dimensions of post-truth society. Originality. It is substantiated that Homo digitalis is the result of a complex set of heterogeneous effects of scientific knowledge, which in modern post-truth conditions appears as different communicative practices. A condition for the formation of a new anthropological type of man in the perspective of scientific and technological progress is the affirmation of ethical wisdom. Conclusions. Knowledge in the process of evolution of socio-cultural life acquires constitutive significance for the process of formation of anthropological situations that manifest themselves in new images of man. Today, he is commensurate with the demands of digital culture, in which human life practices are increasingly becoming information and digital clusters embedded in the reality of a post-truth society. The means of overcoming the passivity of digital man is the formation of a new anthropological type based on a rethinking of the value system. (shrink)

The purpose of the article is the analysis of the causes of the systemic crisis that hit modern civilization through the description of its main structures, identifying the relationship between its elements, assessments of their heuristic potential. This will open up opportunities for finding ways to resolve this crisis, new directions of civilizational development. Theoretical basis of the research are the systems analysis, socio-philosophical and philosophical-anthropological approaches as well as the analysis of scientific developments in the field of global studies. (...) Originality lies in the fact that this article is the first to show the connection between the main structural elements of human civilization as a system. Change in one of the parameters leads to a change in all the others, together with a change in civilization as a whole. Conclusions. The reason for the deep crisis that hit modern civilization is its imbalance as a system. The most important elements of this system are population size, resources and technology, and the core is consciousness in its individual and collective forms. The perception, processing, and use of information, which is a defining civilizational resource, as well as the stability of the entire system depend on the state of consciousness. Consciousness, based on old, obsolete principles and stereotypes, is unable to cope with the most acute challenges of time. New consciousness, since it is formed, will mark the transition to a new theoretical picture of the world and a model of human behavior, in which people will act, driven by proven knowledge, and not willfulness and prejudice. The idea of forming a productive information environment where the ideas of constructiveness and creative work will dominate rather than consumerism and destruction, as is the case at present, must become the categorical imperative of the new consciousness. (shrink)

Purpose. The article suggested for consideration is aimed at clarifying the shift in human perception from the spatial turn announced by Michel Foucault, to a performative turn. The performative turn has an anthropological footing. It is based on the all-round investigation of the body’s principal role for cultural existence, as a result of a reverse reaction to artificial conceptual gap between space and body, which basically means ignoring the embodiment theme. An example of such theoretical deformation was Edmund Husserl’s “anthropology (...) phobia” revealed and thoroughly analysed by Hans Blumenberg in his critical works. Originality of the approach applied in this research, first and foremost, demonstrates not an abstract phenomenological conception as a theoretical construct, but a phenomenological activity itself, as well as practical work expressing antepredicative experience and solving the problems arising in this complicated process. Applying the Blumenberg’s analysis also allows to peep in the sideline notes of Edmund Husserl himself, which, for their part, acquire special meaning in relation to such a practical turn. Conclusions show the following state of affairs demonstrated by the anthropological and performative shift towards the body theme: 1) absolutisation of space without mentioning its relation to body experience is unreasonable and groundless, like in Husserl’s “anthropology phobia ”; 2) since the ground itself is a metaphorical anthropology basis, anthropology can reveal the structural conditions of perception due to thematic fronting of embodiment; 3) this gives anthropology some compensational features, to avoid false culture and nature dualism; 4) so, the space and body relationship is expressed by the Vehikel-phenomenon of the body itself, by placing, arranging and depicting, and thus replacing something missing and unavailable for direct contemplation, by revealing the spatial infrastructure for object perception, creating the presence conditions and metaphorically marking the contemplation boundary; 5) the depicting arrangement is at the same time a bodily performance, a play, staging and performing, which gives an aesthetic, poetic and emphatic impact on the use of philosophy language, in our case, on the way a phenomenology philosopher works with the language. (shrink)

A method of linguistically-oriented reasoning comprehension is proposed. It is based on semiological principles of text comprehension. Both content and form are essential for comprehending argumentative texts. A text recipient is viewed as a rational judge trying to detect all the components of the argument he/she considers and thus to see if the argument is consistent. Elementary and higher level argumentative units of the text are discovered by applying a modified S. Toulmin's model of argumentative functions. Validity and correctness of (...) arguments are established by means of a new – linguistic – interpretation of traditional syllogistic. (shrink)

Purpose. The article suggested for consideration is aimed at clarifying the shift in human perception from the spatial turn announced by Michel Foucault, to a performative turn. The performative turn has an anthropological footing. It is based on the all-round investigation of the body’s principal role for cultural existence, as a result of a reverse reaction to artificial conceptual gap between space and body, which basically means ignoring the embodiment theme. An example of such theoretical deformation was Edmund Husserl’s “anthropology (...) phobia” revealed and thoroughly analysed by Hans Blumenberg in his critical works. Originality of the approach applied in this research, first and foremost, demonstrates not an abstract phenomenological conception as a theoretical construct, but a phenomenological activity itself, as well as practical work expressing antepredicative experience and solving the problems arising in this complicated process. Applying the Blumenberg’s analysis also allows to peep in the sideline notes of Edmund Husserl himself, which, for their part, acquire special meaning in relation to such a practical turn. Conclusions show the following state of affairs demonstrated by the anthropological and performative shift towards the body theme: 1) absolutisation of space without mentioning its relation to body experience is unreasonable and groundless, like in Husserl’s “anthropology phobia ”; 2) since the ground itself is a metaphorical anthropology basis, anthropology can reveal the structural conditions of perception due to thematic fronting of embodiment; 3) this gives anthropology some compensational features, to avoid false culture and nature dualism; 4) so, the space and body relationship is expressed by the Vehikel-phenomenon of the body itself, by placing, arranging and depicting, and thus replacing something missing and unavailable for direct contemplation, by revealing the spatial infrastructure for object perception, creating the presence conditions and metaphorically marking the contemplation boundary; 5) the depicting arrangement is at the same time a bodily performance, a play, staging and performing, which gives an aesthetic, poetic and emphatic impact on the use of philosophy language, in our case, on the way a phenomenology philosopher works with the language. (shrink)