A $\Pi^0_1$ class can be defined as the set of infinite paths through a computable tree. For classes $P$ and $Q$, say that $P$ is Medvedev reducible to $Q$, $P \leq_M Q$, if there is a computably continuous functional mapping $Q$ into $P$. Let $\mathcal{L}_M$ be the lattice of degrees formed by $\Pi^0_1$ subclasses of $2^\omega$ under the Medvedev reducibility. In "Non-branching degrees in the Medvedev lattice of $\Pi \sp{0}\sb{1} classes," I provided a characterization of nonbranching/branching and (...) a classification of the nonbranching degrees. In this paper, I present a similar classification of the branching degrees. In particular, $P$ is separable if there is a clopen set $C$ such that $P \cap C \neq \emptyset \neq P \cap C^c$ and $P \cap C \perp_M P \cap C^c$. By the results in the first paper, separability is an invariant of a Medvedev degree and a degree is branching if and only if it contains a separable member. Further define $P$ to be hyperseparable if, for all such $C$, $P \cap C \perp_M P \cap C^c$ and totally separable if, for all $X,Y \in P$, $X \perp_T Y$. I will show that totally separable implies hyperseparable implies separable and that the reverse implications do not hold, that is, that these are three distinct types of branching degrees. Along the way I will show some related results and present a combinatorial framework for constructing $\Pi^0_1$ classes with priority arguments. (shrink)

I argue that the dual-process account of human learning rejected by Mitchell et al. in the target article is informative and predictive with respect to human behaviour in a way that the authors' purely propositional account is not. Experiments that reveal different patterns of results under conditions that favour either associative or rule-based performance are the way forward.

Predvaritelʹnye zamechanii︠a︡ -- Konformizm, ili Spasenie zdesʹ i seĭchas -- Soprotivlenie, ili Risk -- Nasilie, ili Nakazannai︠a︡ smertʹ -- Gedonizm, ili Poisk utrachennoĭ realʹnosti -- Tradit︠s︡ii︠a︡, ili Prisposablivai︠u︡shcheesi︠a︡ soprotivlenie -- Bessoznatelʹnoe, ili Aksiologicheskai︠a︡ mashina mozga.

A significant characteristic of science today is the extensive utilization of the concept of "probability." Originally it arose in applied fields and was not employed in fundamental research. However, with the development of quantum and statistical physics in the course of the 20th century, the mathematical apparatus of probability theory was widely used in the study of phenomena that obviously could not be studied without it. Thus, it became clear that probability plays a significant role in a scientific world view. (...) Whereas previously it had been regarded merely as a sad consequence of the temporary incompleteness of our knowledge, the time has now come when probability must take its place in the description of the objective regularities of nature. (shrink)

Монография посвящена анализу дискурсов и всех сторон взаимодействия реальности с человеком и особенностями его жизнедеятельности. Адресуется специалистам-языковедам, студентам старших курсов и магистрантам.

Standard Assessment Tasks are used in the assessment of pupil performance relative to the National Curriculum in England and Wales, assigning pupils to one of 10 levels on various Attainment Targets . This is a criterion‐referenced system, and the conventional reliability measures used in norm‐referenced systems do not apply. This paper discusses the problems involved in aggregating SA T items to give levels, and in measuring the reliability of the outcomes produced. Fitting a simple model to SAT data has allowed (...) reliability measures to be produced which are more relevant to this situation than the single numerical values applied to norm‐referenced tests. (shrink)

This is a contribution to the study of the Muchnik and Medvedev lattices of non-empty Π01 subsets of 2ω. In both these lattices, any non-minimum element can be split, i. e. it is the non-trivial join of two other elements. In fact, in the Medvedev case, ifP > MQ, then P can be split above Q. Both of these facts are then generalised to the embedding of arbitrary finite distributive lattices. A consequence of this is that both lattices (...) have decidible ∃-theories. (shrink)

Socio-cultural and political transformations that are taking place in the modern world under the influence of globalization, predetermine the growth of scientific interest in the history and the theory of shaping the group unity.The coverage of various aspects of this problem is found in the works of foreign philosophers (M. Gibernau, S. Huntington, E. Hiddens, B. Yak, et al.), which focus their primary attention on studying the factors, contributing to the emergence of communities in the modern world, while distancing from (...) the development of universal explanatory schemes for the process of forming the collective unity at various stages of the historical development of society.Some Ukrainian researchers (Y. Hrytsak, V. Kravchenko, H. Kasyanov, et al.), who, in contrast to foreign scholars, pay more attention to studying the various aspects of Ukrainian nation-building, are approaching the above problems from a bit different angle of view to solve them. Undoubtedly, the work of these researchers thoroughly and fully covers the history of the formation of the Ukrainian nation, explains the reasons or factors that contributed to its appearance. Meanwhile, they do not have sufficient potential to explain the causes of the cultural fragmentation of modern Ukrainian society, which, in our opinion, has become a logical consequence of the undivided domination in the Ukrainian intellectual discourse of the paradigm of perennialism, within which the cultural identity of the community appears to be a kind of “entity or reality.” Proponents of this position believe that the cultural diversity of nations emerged in the early stages of social development. Within this outlook, Ukrainians, as a mentally and culturally distinct community, have always existed. Of course, their culture has been developing and enriching in the process of historical development and intercultural communication, while its original spiritual and symbolic core remaining unchanged.Despite the fact, that renaissance has a rational grain and can become themethodological basis for very effective national consolidation strategies, one should not ignore its failure to explain the causes of the cultural and civilizational fragmentation of modern Ukrainian society. In our opinion, the solution of this issue requires a comprehensive understanding of the origins, mechanisms and factors, and the formation of a culturally homogeneous Ukrainian cultural space. In view of this, the purpose of our work is to uncover the theoretical preconditions and mechanisms for shaping the cultural identity of Ukrainians in the XIX and early XX centuries. Instead, the task of the work is to highlight the ideological foundations of the growth of scientific interest in folk culture in foreign and Ukrainian intellectual discourse and to reveal their significance in the process of thematizing the modern Ukrainian identity.Methods.The interdisciplinary approach and the principle of unity of the historical and logical have become a methodological basis of scientific research. Methods of historical and philosophical reconstruction, cultural analysis, and extrapolation have been also widely used in the process of research, as well as the fundamental principles of hermeneutics, which have been taken into account.Results. The dominance of the educational enlightenment-cognitive paradigm has contributed to the growth of scientific interest in the cultural identity of peoples, which, according to the prevailing beliefs, has been most clearly preserved in folk poetry and ancient literature. The study of the latter has resulted in the outbreak of ethnographic and linguistic exploration, which facilitated the gradual introduction of the Ukrainian language to literary use, thereby contributing to the thematization of modern Ukrainian identity. (shrink)