This paper calculates, in a precise way, the complexity of the index sets for three classes of computable structures: the class $K_{\omega _{1}^{\mathit{CK}}}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}$ , the class $K_{\omega _{1}^{\mathit{CK}}+1}$ of structures of Scott rank $\omega _{1}^{\mathit{CK}}+1$ , and the class K of all structures of non-computable Scott rank. We show that I(K) is m-complete $\Sigma _{1}^{1},\,I(K_{\omega _{1}^{\mathit{CK}}})$ is m-complete $\Pi _{2}^{0}$ relative to Kleen's O, and $I(K_{\omega _{1}^{\mathit{CK}}+1})$ is m-complete $\Sigma _{2}^{0}$ relative to O.

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

The study of the artistic heritage of neo-academicians in the context of the study of mixed techniques is quite relevant. To date, the analysis of the creativity of artists, representatives of non-academism as an artistic trend of the late twentieth century in Russia, is based on the artistic criticism of art critics, art critics who were part of this trend and considered the work of non-academicians from the perspective of the artistic life of this period in the context of the (...) socio-cultural processes of Russia during the Perestroika era. Also, the works of neo-academist artists are studied from the position of "creative rebellion" and the search for new forms in art. In this article, the works of T. Novikov, G. Guryanov, K. Goncharov, V. Mamyshev-Monroe and other representatives of NAII are studied from the position of "mixed techniques" in art objects. The main emphasis is placed on the analysis of art objects in mixed techniques in the context of overcoming formalism, embodying stylistic diversity, metamorphosis of forms and states, pictorial symbols and universal meanings. The realization of the principle of the infinity of choice and the infinity of meaning and diversity is associated with postmodernism in art, the introduction to which became decisive in Russian art of the late twentieth and early twenty-first centuries. The appeal to the study of art objects of neo-academicians made in mixed technique allows us to enrich and supplement the understanding of the term "mixed techniques" in modern art practices related to the search for new forms, compositional solutions, the formation of a unique author's language, the originality of the work. (shrink)

Purpose. The purpose of the study is to outline the links between individual and collective dimensions of the human worldview. This purpose requires solving two tasks: to update philosophical ideas formed by reflection on human and community worldview; to identify and generalize the relationship of singular and general in the context of the problem of human worldview. Theoretical basis. The study is based on philosophical reflections about manifestations of singular and general worldviews. Such reflections appeared in European philosophy quite a (...) long time ago. Ukrainian and foreign philosophical discourse considers both measures of the worldview. And a role of the carrier of worldview plays either human or society. We can see that in researches of S. Krymskyi, I. Nadolniy, V. Popov, N. Rozhanska, V. Tabachkovskyi, V. Shynkaruk, V. Poythress, D. Rousseau, D. Billingham, C. Gianolla and others. However the links between individual and collective dimensions of worldview are not clearly outlined. It is possible to note the research of V. Popov who focuses on the problem of socio-collective and individual dimensions of worldview. But the scientist focuses more on the use of the concept of worldview in these two meanings. Human as a social being interacts with worldviews of other individuals. That is why we can speak of two dimensions of the worldview function: individual and collective. This problem became topical due to acuteness of the links between human and society in modern life. Originality. The author outlined key links between individual and collective dimensions of human worldview functioning. The study identified a role of human as a carrier of the worldview in formation of collective worldview. Conclusions. Human as a worldview carrier plays a key role in formation of collective worldview. In philosophical discourse thoughts about links between individual and collective worldviews are different and sometimes conflicting. We have a discussion problem of uniformity and diversity of collective worldview. Collective worldview is showed as a circulation of different ideas and views of individuals. But collective worldview is showed as a whole system of individual views too. Collective worldview manifests as integrated phenomenon because it is based on common worldviews of individuals. At the same time the human is influenced by collective worldview in particularly as a past generation heritage. (shrink)

The name of Pavel Ivanovich Novgorodtsev is not very widely known to the reader at large. It has only been in the last ten or twelve years that isolated studies of particular problems in his creative works have begun to appear.

Анализируется круг проблем, к которым было приковано преимущественное внимание русских философов указанного периода. Это - идущее от А. С. Хомякова философское осмысление Божественного Триединства.

The study of orders as a product of spiritual creativity has its long and rich history. In addition to ethnographers, religious scholars, psychologists, philosophers, as well as scientists who carried out their research on the brink of several sciences - M. Bachtin, J. Frezer, K. Levy Briul, worked on their analysis. The orders helped find the keys to the style of thinking of primitive tribes, the peculiarities of their worldview, language, remedies, regulation of social relations.

The institution of the principle of distribution in accordance with work performed in the process of the building of socialism and the consistent implementation of this principle under the conditions of developed socialism are powerful factors in the establishment and consistent implementation of the principle of the universality of work. In the course of the building of communism, payment in accordance with work done will remain the principal source of growth of incomes. Therefore, the completeness of satisfaction of people's requirements (...) and their prosperity depend predominantly on the amount and quality of the work given to society. However, a high level of communist consciousness presumes not merely participation in social labor but a perceived need to work as efficiently and productively as possible. (shrink)