We develop an axiomatic set theory — the Theory of Hyperfinite Sets THS— which is based on the idea of the existence of proper subclasses of large finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS, and present some applications.

It would be no exaggeration to say that our art is presently undergoing a revolutionary stage in its development. The revolutionary renewal that has seized all spheres of life is being ever more forcefully represented in artistic culture as well. That culture is beginning to free itself from bureaucratic regimentation, incompetent pressure from above, inflated authorities, lifeless cliches, and opportunism of the moment. Art is actively seeking its place in perestroika, and is in turn in many respects defining the moral (...) climate of perestroika. Recent works such as Fire [Pozhar] by V. Rasputin, the Sad Detective Story [Pechal'nyi detektiv] by V. Astaf'ev, The Execution Block [Plakha] by Ch. Aitmatov, the paintings of G. Korzhev and V. Sidorov, the sculpture of V. Klykov, etc., are actively working for renewal. (shrink)

We present an axiomatic framework for nonstandard analysis-the Nonstandard Class Theory which extends von Neumann-Godel-Bernays Set Theory by adding a unary predicate symbol St to the language of NBG means that the class X is standard) and axioms-related to it- analogs of Nelson's idealization, standardization and transfer principles. Those principles are formulated as axioms, rather than axiom schemes, so that NCT is finitely axiomatizable. NCT can be considered as a theory of definable classes of Bounded Set Theory by V. Kanovei (...) and M. Reeken. In many aspects NCT resembles the Alternative Set Theory by P. Vopenka. For example there exist semisets in NCT and it can be proved that a set has a standard finite cardinality iff it does not contain any proper subsemiset. Semisets can be considered as external classes in NCT. Thus the saturation principle can be formalized in NCT. (shrink)

We prove that Standardization fails in every nontrivial universe definable in the nonstandard set theory BST, and that a natural characterization of the standard universe is both consistent with and independent of BST. As a consequence we obtain a formulation of nonstandard class theory in the ∈-language.

Iurii Kovalenko.Orthodox theological understanding of church-state relations in Ukraine at the time of development of Media and Information Technology. The author, who for many years was the press-secretary to the Primate of the Ukrainian Orthodox Church, considers continuity UOC position on the principles of church-state relations and their genesis in accordance with the socio-political processes taking place in Ukraine, the development of media and information technology.

v. 1. Recursive model theory -- v. 2. Recursive algebra, analysis and combinatorics.

In the resolution of the Central Committee of the CPSU entitled "On the Periodical Kommunist," the study of the dialectics of the forces and relations of production is assigned to the sphere of economics. It is no accident that the question is posed in this way. Today, under conditions of restructuring, a concrete analysis of the economic connections, contradictions, and interactions of socialist society and of the real forms of manifestation of economic relations is more important than ever. The [current] (...) criticism of erroneous views, widespread in their time, about the exceptional character of the economic system of socialism that made it possible to "constitute" productive relations through the "creative force of the economic plan," is especially timely and substantive. However, a more general sociophilosophical study of the dialectics of the forces and relations of production is also necessary. Lenin's words have never lost their vital force: we cannot take up "particular questions without first solving the general question. …"' It is from these general sociophilosophical positions that we shall be examining some aspects of this topic that we think important. (shrink)

In this research, author analyzes and interprets data of sociological researches of the Razumkov Centre concerning the religious self-identification of Ukrainian citizens, their attitude towards the Church in general and towards the denominations and religions presented in Ukraine in the dynamics from the year 2000 to nowadays. The author also considers external and internal outlook trends and shows a dangerous contradiction between them. As an alternative to solve this conflict, the author suggests the idea of Open Orthodoxy and presents an (...) example of its implementation in projects of the Open Orthodox University of Saint Sophia the Wisdom. (shrink)

The present article analyzes the world order in the past, present and future as well as the main factors, foundations and ideas underlying the maintaining and change of the international and global order. The first two sections investigate the evolution of the world order starting from the ancient times up to the late twentieth century. The third section analyzes the origin and decline of the world order based on the American hegemony. The authors reveal the contradictions of the current unipolar (...) world and explain in what way globalization has become more profitable for the developing countries but not for the developed ones. In the paper also explains the strengthening belief that the US leading status will inevitably weaken. In this connection we discuss the alternatives of the American strategy and the possibility of the renaissance of the American leadership. The last section presents a factor analysis which allows stating that the world is shifting toward a new balance of power and is likely to become the world without a leader. The new world order will consist of a number of large blocks, coalitions and countries acting within a framework of rules and mutual responsibility. However, the transition to a new world order will take certain time (about two decades). This period, which we denote as the epoch of new coalitions, will involve a reconfiguration of the World System and bring an increasing turbulence and conflict intensity. (shrink)

The subject of this research is the period of Russian symphonic music of the 1960s. A new generation of composers – the “Sixtiers” – introduced a fresh modern musical language and remarkable artistic achievements. In first part of the article, the author dwell on several fundamental symphonic works by R. Shchedrin, S. Slonimsky, E. Denisov, Y. Falik, N. Karetnikov, as well gives general characteristics to this period. The second part of the article examines the compositions by A. Schnittke and L. (...) Prigozhin. Special attention is turned to the Symphony No.3 by Boris Tishchenko, who opens new stylistic horizons and encompasses the key trends of modern music, including the avant-garde, into his stylistic orbit. This article is first to consider B. Tishchenko's outstanding Symphony No.3 in the context of stylistic and linguistic innovations of the 1960s, which defines the scientific novelty. Analysis is conducted on the role and place of the youngest composer of the “Sixtiers” B. Tishchenko in the struggle for the “new music”. The conclusion is made that Tishchenko was one of the leaders in revival of the Russian music of the late XX century, and his Symphony No.3 reflects the pursuits of the postwar generation of Soviet composers to the fullest. (shrink)

The subject of the study is the period of Russian symphonic music of the 1960s. A new generation of "sixties" composers has entered the Soviet music scene, imperiously declaring themselves with bright creative achievements, fresh and modern musical language. The epoch of the turning point dictated a new reality, required new artistic thinking, generated diverse creative ideas. The panorama of Russian music was quite colorful, many things in art appeared and disappeared very rapidly, stylistic pluralism, lost at the dawn of (...) Soviet power, returned to the music scene. Special attention is paid to the works of composers of the Leningrad school — S. Slonimsky, Y. Falik, L. Prigozhin and V. Gavrilin. All of them opened new stylistic horizons and absorbed into their sound orbit the main trends of modern music, including the conquests of the Western avant-garde.  The scientific novelty of the work consists in the fact that the author examines the bright and original works of young Leningrad authors in the context of stylistic and linguistic innovations of the 1960s. The article analyzes the role and place of "Sixties" composers in the struggle for "new music". The main conclusion of the article is the idea that the period of musical renewal of the 1960s under consideration turned out to be extremely saturated with the most complex and diverse problems: ideological, general aesthetic, musical style. S. Slonimsky, Y. Falik, L. Prigozhin, V. Gavrilin became undisputed leaders in the renewal of Russian music of the second half of the twentieth century, and their works-"symbols" fully reflected the intense search of the post-war generation of Soviet composers. (shrink)

The subject of this research is the period of Soviet music in the 1960s. A new generation of the composers – the “Sixtiers” – came upon the stage, demonstrating remarkable artistic achievements, fresh and modern musical language. This article is dedicated to the symphonic work of the prominent Russian composer of the late XX century Boris Ivanovich Tishchenko. Particular attention is given to the Symphony No.1, which he created at the age of 22. Tishchenko burst into the Soviet musical space (...) with creative fervor, and asserted himself as a tremendous and unique talent. His extemporaneous music pieces kept pace with the time, in unison with the global changes that took place in Russian symphonism. The scientific novelty lies in consideration of B. Tishchenko’s Symphony No.1 in context of stylistic and linguistic innovations of the 1960s. Detailed analysis is conducted on the role and place of Tishchenko — the youngest of the generation of “Sixtiers” – in the struggle for "new music". The main conclusion lies in the thought that Tishchenko was one of the leaders in the renewal of Russian music in the late XX century, and Symphony No.1 of his early period fully reflected the intense pursuits of the post-war generation of the Soviet composers and opened the path towards the "new shores" in symphonic music of that time. (shrink)

This publication aims to analyze the economic, social, and cultural phenomena that first appeared in the "era of revolutions" that occurred in the nineteenth to early twentieth centuries. The modern European trend toward tolerance, which is the basis of current social and cultural changes, including in our country, has specific intellectual grounds. The subject of the study was the ideosphere of the nineteenth and early twentieth centuries, including philosophical, economic, and psychological concepts that gave rise to modern trends in these (...) areas. The result of this study was the determination of the reasons that caused the change of the ideological paradigm in Europe. The novelty of the research lies in the fact that, for the first time, the intellectual foundations of the formation of tolerance as an actual socio-cultural phenomenon are analyzed. This article consistently proves that among the first such grounds, it is possible to determine the emergence of machine production and, as a result, the appearance of a mass person with a culture corresponding to them, performing a compensatory and entertaining function. The most important cultural foundation is mainly the intellectual "background" created by the teachings of Friedrich Nietzsche, Karl Marx, and Sigmund Freud. The ideas of Anglo-American pragmatism played a significant role in forming a new morality, which included the denial of religion and its values, giving it a utilitarian character. During the subsequent historical period and at present, these views have become the basis for the creation of the so-called "individual faith," in which religion ceases to be the guide of human life but only serves the needs of the individual. The desacralization of religion leads to the study of different aspects of sexuality, which opens up the possibility for modern thinking about gender. The concept of "natural law" should also be attributed to the intellectual factors of the formation of modern European tolerance. (shrink)

The article is devoted to the philosophy of industrial design as the most important area of aesthetic and engineering activity of people, shaping the appearance of modern society. The object of the study is industrial design, and its subject is the philosophical foundations of industrial design. The goal of the study is to identify the philosophical essence of industrial design in epistemological, ontological and anthropological dimensions. Attention is paid to the historical aspects of industrial design, which allows us to more (...) accurately understand the essence of this phenomenon. The author’ also considered modern industrial design, which in its philosophy is characterized by a strong anti-globalist orientation. It is noted that the philosophical understanding of industrial design contributes to the understanding of the features of its historical development. The main conclusion of the study is that industrial design has a certain philosophical content associated not only with the aesthetic side of reality, but also with its axiological and ethical structure. The epistemological problems of industrial design are important: products act as carriers of certain knowledge and concepts and accumulate the cultural experience of mankind. Anthropological problems of design are associated with the model of a human creator and a human recipient of activity. The scientific novelty of the research lies in the understanding of industrial design, which is a systemic object, developing in space and time. In its existence, this object combines presence and “service”, independent givenness and significance for a person. (shrink)

The subject of this study is a set of alleged contradictions in the development of artificial intelligence, pursued in order to achieve their overcoming. Philosophical anthropology contains the potential to analyze complex interactions, to articulate the problems that arise between artificial intelligence and humans. The philosophical and anthropological analysis of artificial intelligence is aimed at understanding this human phenomenon, human presence and its experience. The article is an attempt to identify and outline the trajectories for the possible resolution of the (...) contradiction in the development of artificial intelligence, the analysis of the parameters proposed by philosophical anthropology to solve their problems in the modern socio-cultural situation. The relevance of the proposed problem arises in the fact that artificial intelligence qualitatively changes the existence of a person, and in philosophical anthropology there is a potential to outline the prospects for the development of artificial intelligence, while preserving the languid human in a person. To study this perspective is very important in society. The novelty of the topic raised in the article is the analysis of solving the problems of artificial intelligence from the standpoint of philosophical anthropology, in the articulation of contradictions in the development of artificial intelligence, in the search for solutions to overcome these contradictions. Philosophical anthropology provides tools for a balanced decision on the development of artificial intelligence, the degree of its impact on human existence. (shrink)

The purpose of the study is to identify the needs of bachelor students of various areas in the field of fine arts in the skills of mastering computer graphics and using its various types in professional activities. The Federal State Educational Standard in the areas of education, general and professional competencies associated with the possession of computer graphics, methods and techniques of work necessary for organizing a holistic process in this discipline are analyzed.

According to Becker, the dispute between the intuitionistic (construction as the guarantor of mathematical existence) and the formalistic (non-contradiction as the guarantor of mathematical existence) definition should be resolved in a phenomenological perspective on the problem. The question of the legitimacy of the transfinite should also be resolved in the perspective of a phenomenological constitutive analysis. This analysis provides the key to the problematic of mathematical existence: the result of Becker’s investigations on the logic and ontology of the mathematical is (...) a solution in favour of the “genuine phenomena” of intuitionistic mathematics and the infinite. “Genuine phenomena” are those which turn out to be accessible for constitutive analysis precisely as phenomena of “pure consciousness” and even of the “concrete historical Dasein.” The final solution in favour of the “genuine phenomena” of intuitionistic mathematics and the infinite is motivated by the fact that Hilbert’s formalism does not satisfy the “chief phenomenological principle of demonstrability” (Ausweisbarkeit). (shrink)