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.

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)

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)

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 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 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 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)

We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.

The emergence of Hasidism as a mystical form of the Jewish tradition during the eighteenth century caused organizational divisions in Judaism. This split, which swept half of the Jewish world of Central and Eastern Europe, was largely caused by the extraordinary success of the new religious movement among the common people.Many researchers point to the attractiveness of Hasidism, which was, first and foremost, the over-accessibility of truths proclaimed by the followers of Boal-Shem- This is the founder of the movement. At (...) least the use of moral and instructive sentiments, aphorisms, and even "legendary anecdotes" to express the ideas of Hasidic teachings and their outspoken propaganda among the commoners have made this new movement of the Jewish tradition popularized. Figuratively speaking, the Hasidim sought to fill the inner world of man with properly crafted mystical ideas. (shrink)

The article characterizes post-folklore as a cultural phenomenon of the network society and defines various aspects of its functioning − sociocommunicative, cultural and psychological. The research methodology consisted of a set of basic approaches, principles and methods of scientific research. To achieve the goal, a set of general scientific and special methods was used, including the methods of logical analysis, problemchronological, generalization, synthesis, induction, and analogy.Research results. It has been proven that post-folkloric creativity is important for the development of social (...) communications, as it promotes the exchange of information between users of social networks, conveys people’s knowledge, moods, feelings, and emotions. In the cultural aspect, the works of post-folklore appear as cultural heritage of modern urbanized society and are represented by various types and genres. From the point of view of psychology, post-folklore has an impact on individual and social consciousness, on the development of cognitive processes, etc. The emergence of post-folklore in the field of education is separately mentioned, which indicates its important importance for the formation of the worldview of school youth.Conclusions. Today post-folklore is the subject of scientific research as a phenomenon of mass culture and network society, as a means of social communication, as a phenomenon that has an impact on public and individual consciousness and is gradually being established in the field of education. In the era of accelerated development of information and communication technologies, everyone has the opportunity to become a collector or author of post-folkloric creativity. Further research is planned to be carried out in the direction of studying the prospects for the development of post-folklore in Ukrainian and foreign cultures. (shrink)

Recent years have seen the attention of physicists and philosophers, both at home and abroad, increasingly drawn, as is evident in the professional literature, to the question of the possibility of the existence of particles moving at speeds greater than that of light and to determining the physical and philosophical consequences of this hypothesis. The philosophical consequences have to do primarily with the causality principle. We are in receipt of two articles in which these questions are examined from different perspectives (...) and which supplement each other. (shrink)

The twentieth century brought enormous change to subjects such as language, metaphysics, ethics and epistemology. This volume covers the major developments in these areas and more.

The "mathematization" of knowledge is a historically inevitable process governed by two circumstances. In the first place there is the need for the further extension of knowledge in all areas of human activity, whether it be the study of natural phenomena or the theory of taking decisions in the economic or social sphere. Marx pointed out long ago that a science reaches its highest levels only when it succeeds in making use of mathematics. The second circumstance rendering the process of (...) deepening and broadening the mathematization of knowledge not only necessary but possible lies in the constant development both of mathematics itself and of the technical means broadening the sphere of its application. (shrink)

The topic of consent in paediatrics is made more difficult, and at the same time more interesting, by the complexity of the issues involved and the consequent diversity of viewpoints. In a teaching session for senior medical students on consent in paediatrics it proved necessary to reinstate previous learning from a range of disciplines. Philosophical medical ethics, developmental psychology, communication skills and the appropriate legal definitions all contributed to a proper understanding of the cases presented. The two most important additional (...) components appeared to be a) a basic knowledge of cognitive development and how to apply it, and b) an awareness of the need to balance an individual child's rights or best interests, with those of the family unit, as well as the wider society. (shrink)

This paper presents findings from a longitudinal study of patient refusals (as reported by graduating medical students) to take part in the teaching function of public hospitals. Results from a smaller study of non-patients' attitudes are also reported. Findings are discussed in terms of patients' rights, issues of personal privacy, medical education, and the public good.

Ch. 1. Metodologicheskie problemy sot︠s︡ialʹno-gumanitarnogo poznanii︠a︡ -- ch. 2. Metodologicheskie problemy istorii filosofii i ėstetiki.

In a previous article, the writer explored the geometric foundation of the generally covariant spinor calculus. This geometric reasoning can be extended quite naturally to include the Lie covariant differentiation of spinors. The formulas for the Lie covariant derivatives of spinors, adjoint spinors, and operators in spin space are deduced, and it is observed that the Lie covariant derivative of an operator in spin space must vanish when taken with respect to a Killing vector. The commutator of two Lie covariant (...) derivatives is calculated; it is noted that the result is consistent with the geometric interpretation of the Jacobi identity for vectors. Lie current conservation is seen to spring from the result that the operator of spinor affine covariant differentiation commutes with the operator of spinor Lie covariant differentiation with respect to a Killing vector. It is shown that differentiations of the spinor field defined geometrically are Lorentz-covariant. (shrink)

The relevance of the topic of research of information management as a modern direction of the development of society is that in the 21st century the development of modern civilization has accelerated in the direction of globalization - economic, political, and cultural. The central problem for the development of informational civilization is information as one of the most important attributes and resources of human activity, which grows into knowledge. The problem of research is information management as a science that is (...) not yet sufficiently developed in modern scientific literature; therefore, it is very important to study all new approaches to its development. The purpose of the research is the conceptualization of information management as a science, based on information and communication technologies and informatization mechanisms that help to identify the information and innovation potential of our country, develop information standards and implement intellectual human capital based on information.The article substantiates the essence, tasks and main directions of the development of the concept of information management, determined by informationalism. The transition to a new information civilization has the character of a "technocratic project", based on the innovative development of society, which is based on the information infrastructure. The development of information management is promoted by the "knowledge society", which cultivates a creative person, the formation of which is based on information and knowledge. The research tasks are the conceptualization of information management, its essence, content and main directions of development, which are introduced into the practice of the educational process of high school. The methodological basis for the formation and development of the concept of the information society is informationalism, studied by M. Castells, as well as Autopoese methodology of Maturana and Varela. The results of the research are the formation of the concept of information management as one of the most modern trends in the development of the 21st century society, which is quite innovative, requiring the development of an informative and innovative society and an informative and innovative personality. Conclusions - the concept of information management should be introduced in all areas of the development of society, including high school, which requires the formation of a creative personality as a subject of an informative and innovative society. (shrink)