For a quasi variety of algebras K, the Higman Theorem is said to be true if every recursively presented K-algebra is embeddable into a finitely presented K-algebra; the Generalized Higman Theorem is said to be true if any K-algebra which is recursively presented over its finitely generated subalgebra is embeddable into a K-algebra which is finitely presented over this subalgebra. We suggest certain general conditions on K under which the Higman Theorem implies the Generalized Higman Theorem; a finitely generated K-algebra (...) A is embeddable into every existentially closed K-algebra containing a finitely generated K-algebra B if and only if the word problem for A is Q-reducible to the word problem for B. The quasi varieties of groups, torsion-free groups, and semigroups satisfy these conditions. (shrink)

he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic or antiisomorphic. This (...) algebraic result is new even for ordinary unitriangular groups. The groups elementarily equivalent to a single unitriangular group UTn are studied. If R is a skew field, they are of the form UTn, for some S ≡ R. In general, the situation is not so nice. Examples are constructed demonstrating that such a group need not be a unitriangular group over some ring; moreover, there are rings P and R such that UTn ≡ UTn, but UTn cannot be represented in the form UTn for S ≡ R. We also study the number of models in a power of the theory of a unitriangular group. In particular, we prove that, for any communicative associative ring R and any infinite power λ, I = I). We construct an associative ring such that I = 3 and I) = 2. We also study models of the theory of UTn in the case of categorical R. (shrink)

We consider relational databases organized over an ordered domain with some additional relations — a typical example is the ordered domain of rational numbers together with the operation of addition. In the focus of our study are the first-order queries that are invariant under order-preserving “permutations” — such queries are called order-generic. It has recently been discovered that for some domains order-generic FO queries fail to express more than pure order queries. For example, every order-generic FO query over rational numbers (...) with + can be rewritten without +. For some other domains, however, this is not the case.We provide very general conditions on the FO theory of the domain that ensure the collapse of order-generic extended FO queries to pure order queries over this domain: the Pseudo-finite Homogeneity Property and a stronger Isolation Property. We further distinguish one broad class of domains satisfying the Isolation Property, the so-called quasi-o-minimal domains. This class includes all the o-minimal domains, but also the ordered group of integer numbers and the ordered semigroup of natural numbers, and some other domains.An important difference of this paper from the recent series of related papers is that we generalize all the notions to the case of finitely representable database states — as opposed to finite states — and develop a general lifting technique that, essentially, allows us to extend any result of the kind we are interested in, from finite to finitely representable states. We show, however, that these results cannot be transfered to arbitrary infinite states. (shrink)

For any countable transitive complete theory T with infinite models and the finite model property, we construct a minimal structure M such that the theory of M is small if and only if T is small, and is λ-stable if and only if T is λ-stable. This gives a series of new examples of minimal structures.

This article addresses the famous 1910 debate between Vladimir F. Ern and Semyon L. Frank centered around the problem of identifying the distinguishing features of Russian philosophy. The debate was a continuation of Ern’s debates with Russian philosophers associated with the international journal Logos (Sergei I. Hessen, Fyodor A. Stepun, Boris V. Yakovenko, and others). The author shows that Ern’s understanding of an original Russian philosophy is organically related to his overall philosophical doctrine. As for Frank, his views during the (...) 1910s on the distinguishing features of Russian philosophy were different in nature. It is worth noting that in the 1920s articles written during his émigré period, Frank’s views on the distinguishing features of Russian philosophy undergo a decisive change. Frank’s new ideas about Russian philosophy turn out to be extremely close to those of his late opponent, both on the whole and in the details. At the same time, Frank’s overall philosophical views do not undergo as dramatic a change and develop in a fully evolutionary mode. The author attempts to identify the reason for these changes. (shrink)

We propose that a top priority of the cerebral cortex must be the discovery and explicit representation of the environmental variables that contribute as major factors to environmental regularities. Any neural representation in which such variables are represented only implicitly (thus requiring extra computing to use them) will make the regularities more complex and therefore more difficult, if not impossible, to learn. The task of discovering such important environmental variables is not an easy one, since their existence is only indirectly (...) suggested by the sensory input patterns the cortex receives – these variables are “hidden.” We present a candidate computational strategy for (1) discovering regularity-simplifying environmental variables, (2) learning the regularities, and (3) using regularities in perceptual and decision-making tasks. The SINBAD computational model discovers useful environmental variables through a search for different, but nevertheless highly correlated functions of any kind over non-overlapping subsets of the known variables, this being indicative of some important environmental variable that is responsible for the correlation. We suggest that such a search is performed in the neocortex by the dendritic trees of individual pyramidal cells. According to the SINBAD model, the basic function of each pyramidal cell is (1) to discover and represent one of the regularity-simplifying environmental variables, and (2) to learn to infer the state of its variable from the states of other variables, represented by other pyramidal cells. A network of such cells – each cell just attending to representation of its variable – can function as a sophisticated and useful inferential model of the outside world. (shrink)

This article analyzes changes in the relationship between society and money that are not yet reflected in economic and social theory but have already manifested in cinematic images. Interpreting th...

This article serves as an introduction to central ideas and thoughts formulated by Valery Podoroga. The author undertakes a task of interpreting “anthropogram,” a key tool and procedure developed in Podoroga’s analytical anthropology. In order to clarify this notion, the article discusses a highly original conception of mimesis, first introduced in Podoroga’s book of the same name, as well as Podoroga’s own method of analysis, based on the experience of Russian literature. Examining the important function that the concept of death (...) has in Podoroga’s systematic, the author points to essential links between the philosopher’s mental strategy and the ideas of Russian formalism and deconstruction. The death becomes directly related to the mimetic capacity and deprived of its negative component. This is one more way to overcome metaphysics: to turn death into an analytical tool, which in the space of literature revives the archaic layer of sensuality, where thought and action come to be indistinguishable, and a sign of their plexus is anthropogram. (shrink)

One of the important theological issues for ancient and medieval thought was to account for the existence of evil. Augustine provided an aesthetic explanation: evil exists for contrast, to let the good stand out more prominently. Thus, just as a painting that uses both dark and bright colors, the universe that contains both good and evil is beautiful as a whole. The argument was debated in the twelfth and thirteenth centuries. Alexander of Hales, as well as the Franciscan tradition in (...) general, strongly supported the Augustinian position. The article discusses a previously unknown debate between Albert the Great and Bonaventure about this issue and suggests that Bonaventure is defending his fellow-Franciscan Alexander. (shrink)

R. Pasnau once commented that the present-day academic area of cognitive theory suits medieval thought better than epistemology. The comment seems to the point, and the focus of R. Cross’s book is thus appropriately placed. Scotus’s theory of cognition is worth a new treatment both because Scotus represents a new stage in medieval cognitive theory and because his positions are “sometimes rather fluid” and “not always as clear”. This lack of clarity extends to the most important subject in this book, (...) such as various aspects of the issue of intentionality, where Scotus’s discussion is... (shrink)

This anthology of philosophical texts by Greek and Roman authors brings together works from the late fifth century BC to the sixth century AD that comment on major aesthetic issues such as the perception of beauty and harmony in music and the visual arts, structure and style in literature, and aesthetic judgement. It includes important texts by Plato and Aristotle on the status and the role of the arts in society and in education, and Longinus' reflections on the sublime in (...) literature, in addition to less well-known writings by Philodemus, Cicero, Seneca, Plotinus, Augustine and Proclus. Most of the texts have been newly translated for this volume, and some are available in English for the first time. A detailed introduction traces the development of classical aesthetics from its roots in Platonism and Aristotelianism to its ultimate form in late Antiquity. (shrink)

Franciscan thought in the 1300's, starting with Duns Scotus, is quite a revolution in terms of a shift to relying on sensory and phenomenal experience in the construction of cognitive theories.1 However, we do not yet understand the full extent of its convergence with modern and contemporary thought. In what follows, we intend to advance this understanding. The experiential tendency in early fourteenth-century thought is undermined by a Cartesian-style doubt about the reliability of sensory perception and phenomenal experience that stems (...) from the 63rd proposition of the Condemnations of 1277, which rejects the thesis that "God cannot produce the effect of a secondary cause without the secondary cause itself":2 a... (shrink)

The issue of why God, the Trinity and Christ in Christianity can be called "beautiful" has been muddled in literature on theological aesthetics. John Duns Scotus’s detailed discussion of relations within the Trinity helps resolve this issue. The Trinity can be called "beautiful" in at least three senses, depending on whether one considers Trinitarian relations at all, whether one looks at the relation of equality, or whether one analyzes relations of origin.

The article discusses the relationship between a government and a protest movement, and takes as its chief example the protest movement of Kiev's Maidan. Analyzing the affective logic of community, which is manifested in a crowd, the author argues that this logic is a necessary component of democracy. The argument implies that what are commonly considered democratic values, such as “freedom” and “justice,” are not values, but the effects of the process of resisting any government, the political manifestation of which (...) was described as far back as Hobbes in his description of the state. Having derived the political from these ethical affects, one can produce a nonpolitical definition of democracy in which “freedom,” “justice,” and “dignity” cease to be tools of political rhetoric, pointing to those community relations that cast doubt on the prevailing understanding of the state and politics. (shrink)

The article proposes a universal dual-axis intelligent systems assessment scale. The scale considers the properties of intelligent systems within the environmental context, which develops over time. In contrast to the frequent consideration of the “mind” of artificial intelligent systems on a scale from “weak” to “strong”, we highlight the modulating influences of anticipatory ability on their “brute force”. In addition, the complexity, the ”weight“ of the cognitive task and the ability to critically assess it beforehand determine the actual set of (...) cognitive tools, the use of which provides the best result in these conditions. In fact, the presence of ”common sense“ options is what connects the ability to solve a problem with the correct use of such an ability itself. The degree of ”correctness“ and ”adequacy“ is determined by the combination of a suitable solution with the temporal characteristics of the event, phenomenon, object or subject under study. The proposed approach can be applied in the evaluation of various intelligent agents in different contexts including AI and humans performing complex domain-specific tasks with high uncertainty. (shrink)

A well-known psychologist O. Asmolov speaks of a paradox of system thinking that touches such concepts as "element in the system" and "system in the element", "person in society" and "society in person". The formal logic does not fit the fact that the "person", as an element of the "social system", can not only accommodate the "social system", but potentially can lead to its changes.

We prove that for any k≥3 each element of the h-quasiorder of finite k-labeled forests is definable in the ordinary first order language and, respectively, each element of the h-quasiorder of countable k-labeled forests is definable in the language Lω1ω, in both cases provided that the minimal non-smallest elements are allowed as parameters. As corollaries, we characterize the automorphism groups of both structures and show that the structure of finite k-forests is atomic. Similar results hold true for two other relevant (...) structures: the h-quasiorder of finite k-labeled trees and of finite k-labeled trees with a fixed label of the root element. (shrink)

At first, Bloom's theory appears inimical to empiricism, since he credits very young children with highly sophisticated cognitive resources (e.g., a theory of mind and a belief that real kinds have essences), and he also attacks the empiricist's favoured learning theory, namely, associationism. We suggest that, on the contrary, the empiricist can embrace much of what Bloom says.

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 $\Sigma^0_3$.

A relation on a linearly ordered structure is called semi-bounded if it is definable in an expansion of the structure by bounded relations. We study ultimate behavior of semi-bounded relations in an ordered module M over an ordered commutative ring R such that M/rM is finite for all nonzero r $\epsilon$ R. We consider M as a structure in the language of ordered R-modules augmented by relation symbols for the submodules rM, and prove several quantifier elimination results for semi-bounded relations (...) and functions in M. We show that these quantifier elimination results essentially characterize the ordered modules M with finite indices of the submodules rM. It is proven that (1) any semi-bounded k-ary relation on M is equal, outside a finite union of k-strips, to a k-ary relation quantifier-free definable in M, (2) any semibounded function from $M^{k}$ to M is equal, outside a finite union of k-strips, to a piecewise linear function, and (3) any semi-bounded in M endomorphism of the additive group of M is of the form x $\mapsto \sigmax$ , for some $\mapsto \sigma$ from the field of fractions of R. (shrink)

A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...) ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1. (shrink)

For a signature L with at least one constant symbol, an L‐structure is called minimal if it has no proper substructures. Let be the set of isomorphism types of minimal L‐structures. The elements of can be identified with ultrafilters of the Boolean algebra of quantifier‐free L‐sentences, and therefore one can define a Stone topology on. This topology on generalizes the topology of the space of n‐marked groups. We introduce a natural ultrametric on, and show that the Stone topology on coincides (...) with the topology of the ultrametric space iff the ultrametric space is compact iff L is locally finite (that is, L contains finitely many n‐ary symbols for any ). As one of the applications of compactness of the Stone topology on, we prove compactness of certain classes of metric spaces in the Gromov‐Hausdorff topology. This slightly refines the known result based on Gromov's ideas that any uniformly totally bounded class of compact metric spaces is precompact. (shrink)

A totally ordered group G is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G{±∞}. Continuing work in Belegradek et al. 1115) and Point and Wagner 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. (...) Any pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property ); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions. (shrink)

We prove that any torsion-free, residually finite relatively free group of infinite rank is not \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} -homogeneous. This generalizes Sklinos’ result that a free group of infinite rank is not \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} -homogeneous, and, in particular, gives a new simple proof of that result.

The relevance of the problem under study is due to the need to improve the practical skills and competencies of students in the course of training in order to prepare them for competition with other job seekers in employment. In this regard, this article is aimed at identifying the expediency of students’ participation in competitive selections and grants as a factor that creates conditions for effective practice-oriented learning. The leading method for the study of this problem is a pedagogical experiment, (...) which allows us to comprehensively consider the relationship between students’ participation in competitions and their further self-realization and development as young professionals. The article presents the results of monitoring the behavior of students who received an offer to participate in the university-wide competitive selection of student projects, implemented as part of the Program for Supporting Applied Research and Development of Students and Postgraduates of Petrozavodsk State University. The materials of the article can be useful for teaching staff in building a scheme for teaching students and services involved in the recruitment of personnel for large and medium-sized companies that require young professionals to have practical work skills, teamwork skills and creativity. (shrink)

A careful evaluation of well-documented historical data, along with ancient and modern theological writings, reveals the matriarch Rebekah as one of the most important and controversial individuals of the biblical narrative. Her exceptional beauty, hospitality, morality, faithfulness and sacrificial love were highly admired and praised as iconic by ancient historians, philosophers, the Hebrew community, the Church Fathers and numerous other scholars; yet, some theologians and clerics of the past few 100 years have depicted Rebekah in a negative light. This article (...) intends to highlight this contradiction for the contemporary community of believers by providing an insightful description of the ancient hermeneutics of Rebekah's story. It further aims to encourage biblical scholars to methodologically re-evaluate Rebekah's life, investigating possible reasons as to why the positive image of Rebekah has been overturned in recent years, and thereby determine the cause of such a conceptual paradigm shift in interpreting this key biblical narrative. (shrink)

The research is devoted to the morphology that V.N. Ilyin developed in the work Static and Dynamics of Pure Form and other archival texts. Morphology is central to the philosophy of V.N. Ilyin, but it remains an unexplored subject. The article’s author explores the morphology of the philosopher from a historical and philosophical point of view. In addition to apparent influences (G.W. Leibniz, E. Husserl, N. Lossky), the article’s author revealed the connection of V.N. Ilyin’s ideas with the history of (...) Western European philosophy and his attitude to medieval thinkers. The author considered how V.N. Ilyin understood and assessed his modern philosophy and its results by the middle of the twentieth century. V.N. Ilyin especially paid attention to phenomenology and its connection with morphology, analyzing phenomenology's influence on existential philosophy. In addition to phenomenology, V.N. Ilyin highly appreciated the intuitism of H. Bergson and N. Lossky. The third main philosophical direction in the twentieth century for V.N. Ilyin was religious philosophy (Neo-Thomists and followers of H. Bergson), which aimed at creating axiology, a new system of values. V.N. Ilyin sought to combine various philosophical ideas in the project of morphology based on logic and scientific methodology. He stated the need to reform formal logic and create “metalogic” that would be more consistent with the philosophical tasks of the twentieth century. The morphology of V.N. Ilyin is based on the idea of synthesis and focuses on creating universal science. The comparison of various philosophical ideas of the twentieth century with morphology makes it possible to understand better his philosophical worldview, the course of his reflections, and the meaning of the morphological project. (shrink)

The paper consists of brief literature review of fundamentals and ways of the Russian approach to the studying of the doctrine of love in Latin Patristic IV-V centuries. This topic is peripheral theme for the Russian science; however, it has some development. The literature review describes the most popular ideas and the reasons for their choice.

Department of Philosophy of Religion The Department of Religious Studies of IF NASU during 2006-2008 carried out the specified planned theme. Below we present its sections in the summary. The full study material will be published in the monograph under the same title, which will be published by the end of 2009. The book can be used as a textbook on religious studies.