Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...

Our approach bases on the explication of Rosanov’s creativity as the special intention, that implements the unspeakable Self-Selfness of Vasiliy Rosanov. The ineffability of Self-Selfness can be dialectical expressed by Rosanov through phenomena, of that consists the Rosanov’s world. This ineffability actualizes by Rosanov by means of understanding as a filled emptiness, that determinates the specialties and the structure of the understood objects. The exposition of this emptiness conditions the antinomies of Rosanov’s creativity: one sides is understanding by Rosanov the (...) closed world, other sides it corresponds with the world of things. Rosanov mythically fills the void, using the intimate personal contact with the things. We consider the creativity of Rosanov as the synthesis of both this global directions of Rosanov’s theory: the vision of understanding through things, this vision causes the special perception of things by Rosanov. The things are by Rosanov neither material objects, nor the ideal essences. This are by Rosanov the givens, inherent to the understanding. At the same time Rosanov examines the things through understanding, including it with help of the carnivalisation in his own special world. This method defines in our opinion style and content of Rosanov’s works. The thinker realizes by means of the carnivalisation the understanding, according to the concrete things, creating the special world of life (reality). For Rosanov this world is the second world. (shrink)

Martin-Löf’s type theory stems simultaneously from Frege and Russell’s logic-ontological ideas and Husserl’s phenomenology. The article examines this intermediate status of type theory using as examples Martin-Löf ’s syntactical-semantic method and the role of evidence and canonical objects in his approach. Martin-Löf borrows the syntactical-semantic method from Frege and extends it drawing on Husserl’s theory of meaning. In type theory this method leads to the identity (isomorphism) of syntax and semantics (formal logic and formal ontology). Unlike traditional formal logic the (...) type theory is an interpreted system from the very beginning. Being intuitionistic, Martin-Löf ’s theory is based on the notion of proof, not truth. From the meaning theory point of view, it is a variant of proof-theoretic semantics (Gentzen, Prawitz, Dummett) which understands meaning as an object constructed according to certain rules. So understood, the proof is based on evidence, which allows us to associate it with the theory of intentionality by Husserl. The article compares Martin-Löf ’s type theory with Husserl’s intentionality theory, especially with the latter’s noematic component. We may consider type-theoretical rules for constructing objects and operating with them as a concretization and formalization of the phenomenological notion of noema. Both are explications of the more general concept of meaning. The article discusses the interrelation between notions of sense and meaning (Sinn, Bedeutung) in Frege, Husserl and Martin-Löf. This reveals the uncertainty of Martin-Löf ’s position in relation to meaning theories of Frege and Husserl. (shrink)

The paper aims to prove the hypothesis that Sextus Empiricus’ Neo-Pyrrhonism is significantly influenced by the Cartesian meditation as a genre of philosophizing. It refutes theses about (1) the non-predicativity of Sextus’ language and about (2) Sextus’ epochê as an automatic result of the action of opposite things or statements, and it argues that both Sextus and Descartes distinguish between (a) internal (forced) agreement with clarity and (b) the personal acceptance of this agreement which depends on a volitional decision. Sextus’ (...) recognition of the clarity of appearance as appearance gives Descartes the only chance to refute the skepticism of Sextus, which is invulnerable to external criticism. Therefore, Descartes developed meditation as a special model of purely immanent criticism (the very word “skepticism” is never mentioned in the Meditations), focused on dealing with states of clarity and evidence. The author’s hypothesis is that the key elements to which this model appeals are the “history of a skeptic” set out in Outlines of Pyrrhonism and the conception of skeptical expressions. This hypothesis can be tested further by proving or disproving the thesis that the discourse of I, II, and at least partially of III Meditations is based on the pattern of skeptical expressions, focused on the internal states of the speaker, and not on clarifying the “objective” state of affairs (i.e. not on dogmatic inferences). (shrink)

The spiritual quest of Raymond Lull is of interest to modern philosophical discourse as occupying an intermediate position between the Middle Ages and the Renaissance and thus combining the features of these two eras in the history of the development of human thought. They are connected with the Middle Ages by theocentrism and traditionalism, and with the Renaissance by emphasizing the peculiar polyphony of the world, the predominance of plurality over unity, given in the autonomous dialogic space of the human (...) personality as a gradual immanentization of the presence of a transcendent deity, associated with the acceptance by man of the external world as the only possible one. This immanentization is carried out by Luli in the symbol of Love as the Unity of the Loving and the Beloved, explicating the thinker's introspection. The novelty of the work lies in the application of the teachings of A.F. Losev about the interpretive symbol, which made it possible to consider them as a special form of explication of the personality as its transcendence and simultaneous immanence, being a special form of introspection, which correlates with Lull's teaching about Love as a fluctuation in which the Beloved descends, and the Lover ascends. This contributes to the actualization of Lull's spiritual quest as an integrity, a unique eidos, in which each of the separate features of Raymond Lull's spiritual quest is realized in a special way, reflecting the intermediate position occupied by the thinker between the worlds of Antiquity and the Middle Ages. The proposed model of mutual positing of the "components" of Lull's teaching allows us to show one of the possibilities for the interaction of the thinker's logical system (understanding the force, its bearer and passively perceiving its beginning) and his theologically oriented personal spiritual quest as a special kind of dynamics in which the leading role is assigned to introspection as a personal intentions, a kind of mythological sub-foundation of the actual logical dimension of the thinker's teachings. (shrink)

Introduction. The article examines the dynamics of electoral competition over four electoral cycles from 2005 to 2019 as exemplified by forming representative bodies of local self-government in the city of Chelyabinsk. Particular attention is paid to the impact that the transition of Chelyabinsk to a twotier model of forming local self-government bodies in 2014 had on the electoral competition. The purpose of the paper is to study the dynamics of electoral competition in municipal elections in Chelyabinsk before and after the (...) 2014 reform. Methods. The empirical basis of the study is the database “Electoral competition in the elections of municipal deputies of Chelyabinsk (2005—2019)”, which includes 414 observation units. The analysis of the empirical material is carried out according to the method of G.V. Golosov’s triangle of relative sizes, proposed for classifying party systems and adapted for analyzing elections in single-mandate constituencies. Scientific novelty. The author suggests a methodology for analyzing electoral competition in singlemandate constituencies. For the first time, the phenomenon of “controlled competition” is analyzed on the basis of 4 municipal elections cycles. Results. The analysis makes it possible to speak about fluctuations in electoral competition, its decline in 2009 and 2014 compared to the 2005 elections and increasing by the 2019 elections Conclusions. The “controlled competition” was formed in Chelyabinsk in the period preceding the reform of 2014. The reform introduced a level of local self-government, the effectiveness and necessity of which is not obvious with the existing design of the electoral system. In the course of the reform, the principal-agent model of relations between local self-government bodies and state authorities was finally consolidated. The reform contributed to conserving the “controlled competition”. (shrink)

A Turkish patient with AIDS attempted to commit suicide. Turkey is one of the countries where AIDS education in society and for health personnel has started rather late. This article documents what this patient, his sister and his friends, who helped him to survive for a short while, experienced in the hospital environment. This is a real case history and should be considered from various aspects because suicide was attempted by a person with AIDS who was near the terminal stage. (...) The patient’s friends made a remarkable effort to help him to survive. They were unsure about what to do because they had not respected his wishes and they experienced deep alienation because of the extremely negative attitude of the medical staff. (shrink)

The paper consists of brief literature review of fundamentals and ways of the Russian approach to the studying of the doctrine of love in Latin Patristic IV-V centuries. This topic is peripheral theme for the Russian science; however, it has some development. The literature review describes the most popular ideas and the reasons for their choice.

We propose that a top priority of the cerebral cortex must be the discovery and explicit representation of the environmental variables that contribute as major factors to environmental regularities. Any neural representation in which such variables are represented only implicitly (thus requiring extra computing to use them) will make the regularities more complex and therefore more difficult, if not impossible, to learn. The task of discovering such important environmental variables is not an easy one, since their existence is only indirectly (...) suggested by the sensory input patterns the cortex receives – these variables are “hidden.” We present a candidate computational strategy for (1) discovering regularity-simplifying environmental variables, (2) learning the regularities, and (3) using regularities in perceptual and decision-making tasks. The SINBAD computational model discovers useful environmental variables through a search for different, but nevertheless highly correlated functions of any kind over non-overlapping subsets of the known variables, this being indicative of some important environmental variable that is responsible for the correlation. We suggest that such a search is performed in the neocortex by the dendritic trees of individual pyramidal cells. According to the SINBAD model, the basic function of each pyramidal cell is (1) to discover and represent one of the regularity-simplifying environmental variables, and (2) to learn to infer the state of its variable from the states of other variables, represented by other pyramidal cells. A network of such cells – each cell just attending to representation of its variable – can function as a sophisticated and useful inferential model of the outside world. (shrink)

The relevance of the research reflects the unity of the requirements of the Beijing Philosophical Congress "Learning to be a man" and the anniversary report of the "Rome Club" "Come On! Capitalism, myopia, population and destruction of the planet", which the transformation processes of the socio-sphere are revealed from the standpoint the need for a radical breakdown of the spiritual and moral world of man and his worldview. The foundation of these transformations is the transition in education, as the hippocrine (...) of our knowledge, the source that quenches thirst in them to the "new Enlightenment" as a decisive factor in the learning of a person to be him. This determined the purpose and objectives of the article. The purpose of the article is to substantiate the natural and necessary character of the formation of the "new Enlightenment", to reveal the architectonics of its content. Research objectives : in the context of the goal to uncover the factors that determine the need for a transition in education to the "new Enlightenment", its qualitative difference from the Enlightenment of the 17th-18th centuries; to characterize the new content of "connectedness" in education based on the use of new information technologies; analyze the process of formation of a new spiritual and moral outlook of a specialist on the universal values of humanity; focus the learner’s attention on focusing knowledge of sustainable development as a determining factor of the global problems of mankind through the interrelation of academic disciplines; an important component presents the demand for the formation of a new integral thinking, innovative in its essence and qualitatively different from the analytical one. It is noted that the transition to the path of integral thinking contributes to the connection, coordination and organization into a single whole of the fragments of the object under study. Such thinking is characterized by stability, reliability, variability; it is original in its connections with science and education, and methodological influence on individual and social consciousness. Integral thinking reflects a qualitatively new level of intelligence. Research methods: to achieve the stated goal and constructive solution of the tasks, the article used the method of abduction, analysis and synthesis, historical and logical, synergistic approach. The results of the research: a new paradigm of education is represented – the noospheric-information one corresponding to the factuality of the “new Enlightenment”, as its ability to reproduce itself on a changing scale. The change in the scale of the socio-sphere is due to its globalization processes. The content of the “new Enlightenment” is explicated as a qualitatively new level of formation of students' sustainable knowledge based on the integral innovative type of thinking based on the information resources of society, the use of modern educational technologies, as well as on the values of society, as the quintessence of its wisdom and public intelligence. Conclusions. Thus, the formation of a "new Enlightenment" is natural and necessary. This follows from the requirements of the “learn to be human” program, as well as from the development of an internally ordered education process. “New Enlightenment” also has an attribute of uniqueness, since it does not have anything to compare with, identify; it is an objective, essential, unique phenomenon; it is single, relative, determined by the previous development of education. It is based on the processes of intellectualization, innovation, informational content, humanism and is capable of solving constructively the tasks facing society. (shrink)

The Crimea Conference is by all means an extremely complex historical event. Any attempt to estimate its role and significance without analyzing its ethical components would unavoidably result in unduly simplifying the historical reality of the time, as well as in forming erroneous assumptions that would necessarily be used in the analysis of the causes of Cold War. A thorough examination will show that as far as the ‘ethical’ issues are concerned, there are significant developments with regard to general methodology, (...) as well as its application to the sources. Generations of historians who have addressed the issue of Yalta Conference, although they have not been able to form a scientific, distinct ‘ethical’ tradition so far, have developed all the necessary prerequisites for its establishment. This is evident in the possibility of segmenting the issue in two parts on the one hand, and on the other in the availability of sufficient sources, structured databases, and selected outstanding works. Still, there are no studies about the Yalta Conference so far that address exclusively ethical issues concerning ‘good’ and ‘evil,’ ‘morality,’ ‘duty,’ and ‘honor.’ Although historiographical approaches are to a large extent dependent upon ethical viewpoints, in the case of Yalta agreements so far there have been no techniques available, so as to connect historical accounts with ideology, and historical facts with their philosophical background. In a sense, the situation is quite the same as it is with the study of prehistory: although there is an abundance of data and facts that can be primarily processed, there are no methodological guidelines, nor any devices to classify and explain them. This is also typical for any question raised about the ethics of the Yalta agreements in February 1945. (shrink)

Modern Ukraine is a post-colonial, post-totalitarian state in which decolonization, decommunization, and de-Russification have not yet been fully implemented. This article sets itself the goal of reviewing the agenda of the processes of civilizational transit of Ukraine and developing theoretically grounded vectors of the said process. The important fact that the current stage of development of the “worldview gravity” of Ukrainian society is characterized by an eclectic system of stereotypes is also of significant importance: here coexist both old stereotypes of (...) consciousness and behavior, which have largely ceased to fulfill their functions, and new ones that are unstable and ambiguous. The series of ideas regarding the Ukrainian civilizational choice was already discovered in a monograph, “Civilizational crossroads of modern society,” and presented for Ukrainian readers a few years ago. The current article offers a revision of the previously presented ideas for the international audience of the journal readers, taking into account the current Ukrainian sociocultural situation, at the center of which are the challenges produced by the military aggression of the Russian Federation against Ukraine. The policy of new realism can become an effective tool for social modernization. The given word combination is not accidental: the realism of this type of politics insists on the need for the adequate perception of reality in all its essential aspects, and the novelty emphasizes the need to operate not with the laws and features of the socio-political status quo “in general,” but taking into account the latest dynamics, trends, threats, and problematic challenges. The people and the country need not only (and sometimes not so much) a thorough understanding of their cultural-civilizational, geopolitical, and economic-economic prospects but an indomitable character that guarantees the realization of their potential in spite of anything and against anything. On the difficult path of establishing a civilizational choice, Ukrainians will need not only the awareness of the incomplete state of political modernization, the limited, post-totalitarian (post-colonial, etc.) status, but also to work at the individual level to accelerate evolutionary processes. These processes can catalyze political decisions, not at the declarative level but at the practical level, to fill the steps for the approval of the civilizational choice with content. Step-by-step changes in favor of a new worldview horizon will require significant changes at the personal level through the rejection of destructive post-colonial (post-totalitarian, etc.) narratives in social practice in favor of the development of Ukrainian national identity, which will be preceded by the rational assimilation of the perspectives of civilizational choice, which is a fruitful combination of the European civilizational project and heritage of Ukrainian culture. (shrink)

Recently (2010–2011) new criminal legislation to combat illegal income and corruption was passed and publicly discussed in Lithuania. Within the list of the new legal measures, special attention should be paid to criminalisation of illicit enrichment, establishment of a model of extended property confiscation, reinforcement of responsibility for corruption-related offenses, a provision that not only property but also personal benefits may constitute a bribe. It can be seen from the explanatory letters attached to the draft laws and the political debate (...) that the new regulation is expected to achieve decisive breakthrough in the fight against corruption and illegal income. However, without any doubt as to the necessity to fight against those social evils, the author presents critical evaluation of the reform by applying the test of principles of criminal law, legal language and practical effectiveness. By making critical conclusions that the new criminal legislation deliberately lightens the prosecution’s goal of incrimination and the burden of proof, the author warns about the purposive instrumental nature of the new laws, which are balancing on the threshold of legitimacy. In the article the author reveals crucial shortcomings of the new legislation: in some aspects it lacks legal certainty, in other aspects it ignores the principles of guilt, presumption of innocence and proportionality as well as the conception of criminal law as a last resort (ultima ratio). As a result, the new legal means against illegal income and corruption leave space for applying inadequate repression beyond their intended purpose, in addition, they criminalise human conduct that is insufficiently dangerous and create preconditions for senseless criminal prosecutions and violation of human rights. (shrink)

Сучасні міжнародні відносини переживають глибокі трансформації, тому тісно пов’язана з ними дипломатія також зазнає ґрунтовних змін. її функції, які раніше були фактично прерогативою зовнішньополітичних відомств і здійснювалися переважно посольствами, нині реалізуються через численні державні та недержавні канали. Отже, пов’язана з процесами глобалізації перебудова міжнародних відносин, вихід на світову арену недержавних учасників міжнародних стосунків ставлять перед дипломатією завдання її активного залучення в процес створення нового світового порядку. Водночас силові розв’язання міжнародних проблем виявляються все більш недієвими та небезпечними. В цих умовах саме (...) багатостороння дипломатія є ефективним механізмом урегулювання міжнародних конфліктів і кризових ситуацій. (shrink)

Review of the book Fraisse, G. (1998). Les femmes et leur histoire. Paris: Gallimard.

In Turkey, the foundation of modern dietetic started only in 1935 at the IInd Clinic for Internal Medicine at the Medicine Faculty of Istanbul University on behalf of the clinic's director Sen. Prof. Dr. Erich Frank, a well-known expert on diabetes, and his dietician Elisabeth Wolff, both having refuged from the 1933's Germany. Wolff, one of the early leading and example representatives of the dietetic arising new in the world and Europa at that time, presented and taught the new treatment (...) in Turkey where she worked for 32 years. Frank cooperated intensively with her to establish a modern diabetes treatment with uptodate methods in Turkey. It was her, too, who wrote the first scientifically based book of high practical value in Turkey on the dietary treatment of internal diseases. (shrink)

The article considers possibility of applying the concept of descriptive metaphysics to the project of Kant's transcendental philosophy. According to analytical philosophy, descriptive metaphysics is the description of structures of thinking about the world. The basis for describing acts of thinking about the world from Kant's point of view is the description of forms of intuition. Transcendental (descriptive) analysis of understanding must be preceded by transcendental (descriptive) aesthetics as an investigation of pure intuitions of space and time. Phenomenon of time (...) is considered as a condition for determining the concepts "judgment", "category of understanding", "pure understanding" and "object of knowledge". (shrink)

A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r $\epsilon$ R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations (...) and functions in M. We show that these quantifier elimination results essentially characterize the ordered modules M with finite indices of the submodules rM. It is proven that (1) any semi-bounded k-ary relation on M is equal, outside a finite union of k-strips, to a k-ary relation quantifier-free definable in M, (2) any semibounded function from $M^{k}$ to M is equal, outside a finite union of k-strips, to a piecewise linear function, and (3) any semi-bounded in M endomorphism of the additive group of M is of the form x $\mapsto \sigmax$ , for some $\mapsto \sigma$ from the field of fractions of R. (shrink)

У статті досліджуються проблеми функціонування газового ринку України в контексті критеріїв ефективності, відкритості, транспарентності, міжнародної конкурентоспроможності. Оцінений потенціал нарощування власного видобутку газу із традиційних та нетрадиційних джерел з урахуванням природно-ресурсних, технологічних, соціально-економічних, управлінських і геополітичних факторів. Окреслені шляхи розвитку розвідки, видобутку, транспортування, зберігання й дистрибуції природного газу. Обґрунтована необхідність розширення та організаційно-правового оформлення міжнародного співробітництва зі світовими ТНК у цих сферах. Підкреслено критичну значущість для України активної політики енергоефективності й газозаміщення.

The article investigates the problem of the correlation between sense and communicative situation which characterizes philosophical and scientific texts. The analysis of ancient genre of “table-talk", which goes back to Plato's dialogue “Banquet", shows that the dialogue as a text construction form defines the philosophical sense of the text in coordination with communication features of a real table-talk (symposion). This communicative mechanism coordinates text (dialogue) and reality (symposion), and its action can be clarified by “format of text" concept. It is (...) determined by three essential characteristics of the text: the circumstances of his generation, communicative situation between the author and the reader, and the form of the text. The variety of formats in every cultural and historical situation is determined, in its turn, by the actual text culture.dentification and analysis of symposion format allows to trace the transformation of its textual expression of “Table Talk" through “aphorisms" of modern times to modern “abstract" and “round table materials". It is noted that the process of cultural transformation of the text reflects the changes in the social reality of the transition from the ancient symposion to the French salon in the seventeenth century and further to modern symposium. It is revealed the basic feature of the modern version of symposion format that is convergence, and sometimes interference of communicative and public dimensions of the text. (shrink)

In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $$ {\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $$ {\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...) $$\textbf{D}$$ D. Although we focus on the smallest discussive logic and its correspondence to $$ {\textsf {D}}_{\textsf {2}}$$ D 2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of $$ {\textsf {D}}_{\textsf {0}}$$ D 0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. $$ {\textsf {D}}_{\textsf {0}}$$ D 0 understood as a set of theses is contained in $$ {\textsf {D}}_{\textsf {2}}$$ D 2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains $$ {\textsf {D}}_{\textsf {0}}$$ D 0. (shrink)

Publication date: 2 May 2019 Source: Author: Oleg Tarnopolsky The article discusses an innovative course taught to students majoring in English at Ukrainian universities. The course called “Specific Features of the English Language and English-Speaking Nations’ Cultures in the Context of International Communication” was designed to eliminate the lack of a number of issues that must be included in the curriculum of English language and culture studies to be learned by such students but which are ordinarily not included there (...) because each of them cannot make the subject matter of a separate university course and does not fit into the traditionally taught courses. The issues in question embrace: the specific role of English among other languages of international communication; World Englishes, International English and English as a lingua franca and how to choose the variety of English to be taught as a foreign language; the specifics of business negotiations in English in intercultural contexts, business presentations in English, and business telephoning in English in such contexts; communicative behavioral etiquette in intercultural communication in English; lifestyle communicative behavioral patterns of the English-speaking nations. The paper shows how teaching these issues enriches and improves the English language and culture education of English major students expanding that education and relevant practical training to fit much better the international and intercultural contexts of communication in English. (shrink)

In many films, story is presented in an order different from chronological. Deviations from the chronological order in a narrative are called anachronies. Narratological theory and the evidence from psychological experiments indicate that anachronies allow stories to be more interesting, as the non-chronological order evokes curiosity in viewers. In this paper we investigate the historical dynamics in the use of anachronies in film. Particularly, we follow the cultural attraction theory that suggests that, given certain conditions, cultural evolution should conform to (...) our cognitive preferences. We study this on a corpus of 80 most popular mystery films released in 1970–2009. We observe that anachronies have become used more frequently, and in a greater proportion of films. We also find that films that made substantial use of anachronies, on average, distributed the anachronies evenly along film length, while the films that made little use of anachronies placed them near the beginning and end. We argue that this can reflect a functional difference between these two types of using anachronies. The paper adds further support to the argument that popular culture may be influenced to a significant degree by our cognitive biases. (shrink)

Primatological and archaeological evidence along with anthropological accounts of hunter-gatherer societies indicate that lethal between-group violence may have been sufficiently frequent during our ancestral past to have shaped our evolved behavioral repertoire. Two simulations explore the possibility that heroism (risking one's life fighting for the group) evolved as a specialized form of altruism in response to war. We show that war selects strongly for heroism but only weakly for a domain-general altruistic propensity that promotes both heroism and other privately costly, (...) group-benefiting behaviors. A complementary analytical model shows that domain-specific heroism should evolve more readily when groups are small and mortality in defeated groups is high, features that are plausibly characteristic of our collective ancestral past. (shrink)

he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic or antiisomorphic. This (...) algebraic result is new even for ordinary unitriangular groups. The groups elementarily equivalent to a single unitriangular group UTn are studied. If R is a skew field, they are of the form UTn, for some S ≡ R. In general, the situation is not so nice. Examples are constructed demonstrating that such a group need not be a unitriangular group over some ring; moreover, there are rings P and R such that UTn ≡ UTn, but UTn cannot be represented in the form UTn for S ≡ R. We also study the number of models in a power of the theory of a unitriangular group. In particular, we prove that, for any communicative associative ring R and any infinite power λ, I = I). We construct an associative ring such that I = 3 and I) = 2. We also study models of the theory of UTn in the case of categorical R. (shrink)