The discussion of problems of contradiction in the development of the socialist economy has not thus far brought scholars to an agreed opinion on this question. The thought has been expressed in this regard that to frame the question as one of defining a basic contradiction of socialism is false and that under socialism only partial and temporary contradictions can occur, which spring up and are resolved in various periods of the development of socialist society.

We present some equivalent conditions for a quasivariety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}$$\end{document} of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf A}, {\bf B} \in \mathcal {K}}$$\end{document} are nontrivial, then there exists \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf C} \in \mathcal{K}}$$\end{document} (...) such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{K}}$$\end{document} is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5]. (shrink)

The fundamental question in reverse mathematics is to determine which set existence axioms are required to prove particular theorems of mathematics. In addition to being interesting in their own right, answers to this question have consequences in both effective mathematics and the foundations of mathematics. Before discussing these consequences, we need to be more specific about the motivating question.Reverse mathematics is useful for studying theorems of either countable or essentially countable mathematics. Essentially countable mathematics is a vague term that is (...) best explained by an example. Complete separable metric spaces are essentially countable because, although the spaces may be uncountable, they can be understood in terms of a countable basis. Simpson gives the following list of areas which can be analyzed by reverse mathematics: number theory, geometry, calculus, differential equations, real and complex analysis, combinatorics, countable algebra, separable Banach spaces, computability theory, and the topology of complete separable metric spaces. Reverse mathematics is less suited to theorems of abstract functional analysis, abstract set theory, universal algebra, or general topology.Section 2 introduces the major subsystems of second order arithmetic used in reverse mathematics: RCA0, WKL0, ACA0, ATR0 and – CA0. Sections 3 through 7 consider various theorems of ordered group theory from the perspective of reverse mathematics. Among the results considered are theorems on ordered quotient groups, groups and semigroup conditions which imply orderability, the orderability of free groups, Hölder's Theorem, Mal'tsev's classification of the order types of countable ordered groups. (shrink)

In this work, we study computable families of Turing degrees introduced and first studied by Arslanov and their numberings. We show that there exist finite families of Turing c.e. degrees both those with and without computable principal numberings and that every computable principal numbering of a family of Turing degrees is complete with respect to any element of the family. We also show that every computable family of Turing degrees has a complete with respect to each of its elements computable (...) numbering even if it has no principal numberings. It follows from results by Mal’tsev and Ershov that complete numberings have nice programming tools and computational properties such as Kleene’s recursion theorems, Rice’s theorem, Visser’s ADN theorem, etc. Thus, every computable family of Turing degrees has a computable numbering with these properties. Finally, we prove that the Rogers semilattice of each such non-empty non-singleton family is infinite and is not a lattice. (shrink)

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra (...) and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be useful for not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science. (shrink)

t. 1. Klassicheskai︠a︡ algebra.--t. 2. Matematicheskai︠a︡ logika i obshchai︠a︡ teorii︠a︡ algebraicheskikh sistem.

Mal Leicester; Collective Moral Philosophy and Education for Pluralism: a replay to Graham Haydon, Journal of Philosophy of Education, Volume 20, Issue 2, 30 Ma.

This volume examines the conflicting factors that shape the content and form of grammatical rules in language, which speakers and addressees need to contend with when expressing themselves and when trying to comprehend messages. Chapters examine adult language, first and second language acquisition, and the motivations behind historical change.

This paper is a response to papers by Wilson, Burwood and White concerning equal opportunities as an educational ideal. I seek to legitimate this ideal, in contrast to these earlier attempts to persuade us that it is incoherent, unreasonable or misguided. I argue that, given the social context in which the term is used, it is meaningful and represents rational and praiseworthy goals. I identify four aspects of ‘equal opportunities’ and conclude that the concern to promote such opportunities arises from (...) desire for a more just educational provision and out of concern for the well-being of children in oppressed groups. (shrink)

La Modernidad afirma la autonomía del mundo. Pero amigos y enemigos siguen operando con el prejuicio mitológico de un intervencionismo divino: si Dios quisiera, no habría mal y el mundo sería perfecto. El dilema de Epicuro, asimilable en una cultura de fe ambiental, se convierte en dificultad insuperable en la nueva «era crítica», y Kant —preso él mismo del prejuicio— proclama el fracaso de la teodicea. Fracaso para los creyentes, pues resulta increíble un dios que pudiendo no quiere o que (...) queriendo no puede. Fracaso para el ateísmo moderno que se apoya en el mal, pues atribuyéndolo a Dios niega la autonomía del mundo. Pero el fracaso kantiano afecta sólo a la teodicea pre-crítica en un mundo secular. El propósito del presente libro es «repensar el mal» tomando con toda consecuencia la secularidad. Partiendo del mundo, como si Dios no existiese, obliga a empezar desde abajo, respetando la autonomía de su funcionamiento. Entonces el problema —por primera vez en su historia— se estructura en tres pasos distintos. La ponerología muestra que la finitud, constitutivamente carencial y contradictoria, hace inevitable la aparición del mal. La pisteodicea, desde este resultado, señala que toda visión del mal es una respuesta, una «fe» que debe justificarse: sea náusea sartriana o esperanza religiosa. La teodicea es entonces la «pisteodicea» cristiana, que ahora puede romper el dilema, lograr la coherencia y presentar a Dios como el Anti-mal. Nace así una visión que distingue entre una «vía corta» (el fondo verdadero de la visión antigua, apoyada en la confianza) y una «vía larga» (con los tres pasos) de la teodicea; insiste en la «lógica del a-pesar-de» frente a cualquier finalismo del mal; responde a la dificultad del «demasiado mal» o posibilidad de salvación escatológica, y, finalmente, actualiza la comprensión de temas tan vivos como el pecado original, la providencia, el milagro, la oración de petición, el holocausto y el infierno. (shrink)

En este libro, la autora desarrolla su concepción del juicio reflexionante inspirada en Emmanuel Kant y en Hannah Arendt para concentrarse en cómo cierto tipo de narraciones modelan nuestras nociones de lo que consideramos moral. Lara nos ofrece distintas concepciones sobre el mal en su formulación histórica mediante los ejemplos de las tragedias griegas, las diferentes concepciones sobre el mal en la obra de Shakespeare, el uso literario de la metáfora en la obra de Joseph Conrad y en narraciones fílmicas (...) que describen la crueldad humana. Lara sugiere que el aprendizaje moral es un proceso en el que intervienen las instituciones sociales, la voluntad de los individuos y de las sociedades para comprometerse a un debate abierto y con ello modelar los juicios colectivos sobre el pasado. Lara enfatiza que el juicio reflexionante se da entre un evento, una narración de dicho evento y la recepción pública de dicha narrativa. En este libro se aportan importantes métodos para la comprensión del fenómeno moral del mal, porque introducen nuevas verdades desvelatorias acerca de eventos particulares que no pueden ser simplemente captados por medio de categorías conceptuales. Lara utiliza como fuentes a Jürgen Habermas, Walter Benjamin, Primo Levi, Giorgio Agamben y Ariel Dorfman para probar la conclusión de este tipo de narraciones: la acción (de crueldad) ata de manera definitiva al perpetrador con su víctima. (shrink)