A Guide to Classical and Modern Model Theory, Marcja Annalisa, Toffalori Carlo
Автор: Kechris Название: Classical Descriptive Set Theory ISBN: 0387943749 ISBN-13(EAN): 9780387943749 Издательство: Springer Рейтинг: Цена: 6265 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.
Описание: This volume contains a variety of problems from classical set theory. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. The problems vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.
Автор: Ribenboim Название: The Theory of Classical Valuations ISBN: 0387985255 ISBN-13(EAN): 9780387985251 Издательство: Springer Рейтинг: Цена: 17241 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory. These are the topics which are the object of this book.
Описание: The thirteen articles brought together in this volume explore key aspects of the transmission of learning and the transformation of thought from the late Middle Ages to the early modern period. Focusing on important topics in early modern metaphysics, philosophical theology, and modal theory, the contributions gathered here view developments in the early modern period against the backdrop of late-medieval scholasticism. This approach not only reveals the continuity of Western intellectual life in a period of profound change, but also makes it possible to identify with precision what is original in early modern thought. The topics dealt with include metaphysics as a science, the rise of probabilistic modality, freedom of the human will, as well as the role and validity of logical reasoning in speculative theology. The volume will be of interest to scholars who work on medieval and early modern philosophy, theology, and intellectual history.
Описание: This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.
Автор: Poizat Название: A Course in Model Theory ISBN: 0387986553 ISBN-13(EAN): 9780387986555 Издательство: Springer Рейтинг: Цена: 6265 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Translated from the French, this book presents an introduction to first-order model theory. Starting from scratch, it reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It introduces logic via the study of the models of arithmetic.
Описание: The requirement to reason logically forms the basis of all mathematics, and hence mathematical logic is one of the most fundamental topics that students study. Assuming no prior knowledge of the topic, this book provides an introduction for advanced undergraduate students. The concept of model underlies the text, giving it a theoretical coherence.
Описание: Galois theory is one of the most beautiful subjects in mathematics, but it is heard to appreciate this fact fully without seeing specific examples. Numerous examples are therefore included throughout the text, in the hope that they will lead to a deeper understanding and genuine appreciation of the more abstract and advanced literature on Galois theory. This book is intended for beginning graduate students who already have some background in algebra, including some elementary theory of groups, rings and fields. The expositions and proofs are intended to present Galois theory in as simple a manner as possible, sometimes at the expense of brevity. The book is for students and intends to make them take an active part in mathematics rather than merely read, nod their heads at appropriate places, skip the exercises, and continue on to the next section.
Автор: P. Odifreddi Название: Classical Recursion Theory, ISBN: 0444894837 ISBN-13(EAN): 9780444894830 Издательство: Elsevier Science Рейтинг: Цена: 7832 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Includes a number of applications to logic (in particular Godel`s theorems) and to computer science, for which Recursion Theory provides the theoretical foundation. This book presents a comprehensive reference for the subject starting from first principles.
Автор: Charles Robert Hadlock Название: Field Theory and its Classical Problems ISBN: 088385032X ISBN-13(EAN): 9780883850329 Издательство: Cambridge Academ Рейтинг: Цена: 3335 р. Наличие на складе: Поставка под заказ.
Описание: Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of e and ?, cyclotomic polynomials, polynomials over the integers, Hilbert’s irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.
Автор: P. Odifreddi Название: Classical Recursion Theory, Volume II, ISBN: 044450205X ISBN-13(EAN): 9780444502056 Издательство: Elsevier Science Рейтинг: Цена: 14944 р. Наличие на складе: Поставка под заказ.
Описание: Describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. This book presents a detailed picture of the computable sets from the perspective of theoretical computer science. It is suitable for those interested in complexity and computability theory.
Описание: Introduction to Modern Number Theory surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
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