Intermediate prepositional logics we consider here describe the setI() of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI() is a Heyting algebra. This algebra gives rise to the logic of infinite problems from [13] denoted here asLM 1. Some other definitions of negation inI() lead to logicsLM n (n ). We study inclusions between these and other systems, proveLM n to be non-finitely axiomatizable (n ) and recursively axiomatizable (n ). We also show that formulas (...) in one variable do not separateLM from Heyting's logicH, andLM n (n ) from Scott's logic (H+S). (shrink)

There is a Turing computable embedding $\Phi $ of directed graphs $\mathcal {A}$ in undirected graphs. Moreover, there is a fixed tuple of formulas that give a uniform effective interpretation; i.e., for all directed graphs $\mathcal {A}$, these formulas interpret $\mathcal {A}$ in $\Phi $. It follows that $\mathcal {A}$ is Medvedev reducible to $\Phi $ uniformly; i.e., $\mathcal {A}\leq _s\Phi $ with a fixed Turing operator that serves for all $\mathcal {A}$. We observe that there is a graph (...) G that is not Medvedev reducible to any linear ordering. Hence, G is not effectively interpreted in any linear ordering. Similarly, there is a graph that is not interpreted in any linear ordering using computable $\Sigma _2$ formulas. Any graph can be interpreted in a linear ordering using computable $\Sigma _3$ formulas. Friedman and Stanley [4] gave a Turing computable embedding L of directed graphs in linear orderings. We show that there is no fixed tuple of $L_{\omega _1\omega }$ -formulas that, for all G, interpret the input graph G in the output linear ordering $L$. Harrison-Trainor and Montalbán [7] have also shown this, by a quite different proof. (shrink)

Two decades of independence of Ukraine and the free development of Ukrainian Christianity in Kyiv traditions indicate that the time of the underground life of the Ukrainian Greek Catholic Church and the communist past of Ukrainian Christians in general left deep marks in their souls and mentality and throughout Ukrainian society. New social problems, especially of a social and economic nature, have generated in this society a number of new spiritual and social negative phenomena and challenges that the Church is (...) looking for explanations and answers: a significant dominance of people in the material purpose and its negative impact on their spiritual freedom; the inner spiritual conflict in the souls of people between religious and secular consciousness ; the need for spiritual and social equilibrium and interconfessional understanding; the latest practical atheism; the phenomenon of the so-called "man of the Soviet" - "homo sovietikus", which manifests itself in the distortion of the representatives of this group of people historically established and traditional for the pre-Soviet period and restored rudiments during the independence of Ukraine of the Ukrainian social-spiritual worldview and religious mentality. Therefore, Ukrainian Christianity, in particular Ukrainian Catholicism, faces the task of realizing Christian "reinclusion" and the new evangelization of Ukrainian society to overcome the consequences of the atheistic Soviet past, which should be based on the experience of the Universal Church. (shrink)

Introduction. The relevance of the topic of the article is conditioned, on the one hand, by the necessity to assess the effectiveness of using the managerial potential of the key employees at the coal industry enterprises in Russia, on the other hand, by the lack of a scientific and methodological basis for solving the problem. The gap will not allow Russian coal companies to master the trajectory of sustainable economic development in the near future. The purpose of the article is (...) to develop a methodological approach to assessing the effectiveness of using the managerial potential of key employees in the coal industry. Methods. The author uses the methods of systemic, semantic and retrospective analysis, as well as benchmarking. Scientific novelty of the research. The author proposes a methodological approach to assessing and forecasting the effectiveness of using the managerial potential of key employees, a distinctive feature of which is determining the congruence of the internal competitive environment of a coal mining enterprise to its external environment. Results. The outlined approach to assessing the effectiveness of using the managerial potential of key employees makes it possible to predict and plan the trajectory of its development, taking into account the congruence of the internal competitive environment of an enterprise to the external environment, an innovative market economy. Conclusions. On the basis of the obtained quantitative results of assessing the effectiveness of using the managerial potential of key employees, the author concludes that there are significant opportunities to increase the level of managers’ competitiveness and the sustainable operation of coal industry enterprises in Russia, the implementation of which is achieved by the balanced development of managerial potential and strengthening the congruence of the internal competitive environment of an enterprise. (shrink)

'This book is a masterpiece of theoretical thought. It anticipates the actual achievements of much of what we now call sociolinguistics.

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

We carry out some of Galois' work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions F ≤ K ≤ L. This exposition of a special case of [10] has the advantage (...) of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms. (shrink)

Name der Zeitschrift: Byzantinische Zeitschrift Jahrgang: 109 Heft: 2 Seiten: 821-836.

This paper began as a generalization of a part of the author's PhD thesis about ACFA and ended up with a characterization of groups definable in T A . The thesis concerns minimal formulae of the form x ∈ A ∧ σ(x) = f(x) for an algebraic curve A and a dominant rational function f: A → σ(A). These are shown to be uniform in the Zilber trichotomy, and the pairs (A, f) that fall into each of the three cases (...) are characterized. These characterizations are definable in families. This paper covers approximately half of the thesis, namely those parts of it which can be made purely model-theoretic by moving from ACFA, the model companion of the class of algebraically closed fields with an endomorphism, to T A , the model companion of the class of models of an arbitrary totally-transcendental theory T with an injective endomorphism, if this model-companion exists. A T A analog of the characterization of groups definable in ACFA is obtained in the process. The full characterization of the cases of the Zilber trichotomy in the thesis is obtained from these intermediate results with heavy use of algebraic geometry. (shrink)

In this article, cognitivism is understood as the view that the engine of human (individual and collective) action is the intentional, dispositional, or other mental capacities of the brain or the mind. Cognitivism has been criticized for considering the essence of human action to reside in its alleged source in mental processes at the expense of the social surroundings of the action, criticism that has often been inspired by Ludwig Wittgenstein's later philosophy. This article explores the logical extent of the (...) critique of cognitivism, arguing that by positing collectively shared knowledge of criteria as the engine of human action many such critiques themselves display latent cognitivism. (shrink)

In this article, cognitivism is understood as the view that the engine of human action is the intentional, dispositional, or other mental capacities of the brain or the mind. Cognitivism has been criticized for considering the essence of human action to reside in its alleged source in mental processes at the expense of the social surroundings of the action, criticism that has often been inspired by Ludwig Wittgenstein's later philosophy. This article explores the logical extent of the critique of cognitivism, (...) arguing that by positing collectively shared knowledge of criteria as the engine of human action many such critiques themselves display latent cognitivism. (shrink)

Ocherk 1. Voprosy ontologii -- Ocherk 2. Voprosy ėtiki i ėstetiki -- Ocherk 3. Voprosy gnoseologii i aksiologii.