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.

We report a magnetization, magnetostriction, electrical resistivity, specific heat and neutron scattering study of a UNi 2/3 Rh 1/3 Al single crystal, a solid solution of an antiferromagnet UNiAl and a ferromagnet URhAl. The huge uniaxial magnetic anisotropy confining the principal magnetic response to the c axis in the parent compounds persists also for the solid solution. The magnetization curve at 1.6 K has a pronounced S shape with an inflection at 12 T. The temperature dependence of magnetic susceptibility exhibits (...) a maximum around 10 K and is magnetic history dependent at lower temperatures where the resistivity increases linearly with decreasing temperature. The low-temperature „ anomaly is removed in a magnetic field applied along c , which yields a large negative magnetoresistance amounting to m 46 z in 14 T . The C/T values exhibit a minimum around 12 K and below 8 K they become nearly constant , which is strongly affected by magnetic fields. Neutron scattering data confirm a non-magnetic ground state of UNi 2/3 Rh 1/3 Al. The bulk properties at low temperatures are tentatively attributed to the freezing of U magnetic moments with antiferromagnetic correlations. The additional intensities detected on top of nuclear reflections in neutron diffraction in a magnetic field applied along c are found to be proportional to the field-induced magnetization, which reflects field-induced ferromagnetic coupling of U magnetic moments. This scenario is corroborated also by finding low-temperature magnetostriction data that also scale with the square of magnetization. (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)

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)

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)

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.

The problems of clarifying the fundamental logical and mathe­matical concepts, and hence of accomplishing a truly radical grounding of logic and mathematics, were precisely what motivated the very beginnings of Husserl’s phenomenology. This paper is divided into two main parts. The first part focuses on the meaning and structure of Husserl’s explanation of the “logical and psychological” nature of fundamental arithmetical concepts. Particular emphasis is placed on the strategy of Philosophy of Arithmetics (1891) of analysing cardinal numbers in concepts (pivotal (...) yet just as much harmful to philosophy) such as Vorstellungen, mental phenomena and repre­sentations. Together with Arend Heyting and Hermann Weyl, it was the phenomenologist-mathematician Oskar Becker who was the main actor in the second round in the complex dialogue between meta-mathematics and phenomenological philosophy. The second part of this paper aims to clarify Becker’s attempt to apply the theory of actualization of intentionality to the problem of the mode of being of the mathematical and the criterion of mathematical existence. (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 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.

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)

To begin with, can we possibly call esthetic activity a cognitive function , that is, do the products of esthetic activity possess, along with their other characteristics, a certain cognitive value?