A Course in Model Theory

Author: Katrin Tent,Martin Ziegler

Publisher: Cambridge University Press

ISBN: 052176324X

Category: Mathematics

Page: 248

View: 461

DOWNLOAD NOW »

This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

A Course in Model Theory

An Introduction to Contemporary Mathematical Logic

Author: Bruno Poizat

Publisher: Springer Science & Business Media

ISBN: 9780387986555

Category: Mathematics

Page: 443

View: 2362

DOWNLOAD NOW »

This book, translated from the French, is an introduction to first-order model theory. The first six chapters are very basic: starting from scratch, they quickly reach the essential, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. The next chapter introduces logic via the study of the models of arithmetic, and the following is a combinatorial tool-box preparing for the chapters on saturated and prime models. The last ten chapters form a rather complete but nevertheless accessible exposition of stability theory, which is the core of the subject.

Model Theory in Algebra, Analysis and Arithmetic

Cetraro, Italy 2012, Editors: H. Dugald Macpherson, Carlo Toffalori

Author: Lou van den Dries,Jochen Koenigsmann,H. Dugald Macpherson,Anand Pillay,Carlo Toffalori,Alex J. Wilkie

Publisher: Springer

ISBN: 3642549365

Category: Mathematics

Page: 195

View: 2880

DOWNLOAD NOW »

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Mathematical Logic and Model Theory

A Brief Introduction

Author: Alexander Prestel,Charles N. Delzell

Publisher: Springer Science & Business Media

ISBN: 1447121767

Category: Mathematics

Page: 194

View: 8573

DOWNLOAD NOW »

Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.

Sets, Models and Proofs

Author: Ieke Moerdijk,Jaap van Oosten

Publisher: Springer

ISBN: 3319924141

Category: Mathematics

Page: 141

View: 7930

DOWNLOAD NOW »

This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

Models, Logics, and Higher-dimensional Categories

A Tribute to the Work of Mihály Makkai

Author: Bradd T. Hart

Publisher: American Mathematical Soc.

ISBN: 0821883828

Category: Mathematics

Page: 426

View: 4708

DOWNLOAD NOW »

Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.

Lectures in Logic and Set Theory: Volume 2, Set Theory

Author: George Tourlakis

Publisher: Cambridge University Press

ISBN: 9781139439435

Category: Mathematics

Page: N.A

View: 7768

DOWNLOAD NOW »

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Essential Stability Theory

Author: Steven Buechler

Publisher: Cambridge University Press

ISBN: 1107168392

Category: Mathematics

Page: 367

View: 3801

DOWNLOAD NOW »

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Stability theory was introduced and matured in the 1960s and 1970s. Today stability theory influences and is influenced by number theory, algebraic group theory, Riemann surfaces, and representation theory of modules. There is little model theory today that does not involve the methods of stability theory. In this volume, the fourth publication in the Perspectives in Logic series, Steven Buechler bridges the gap between a first-year graduate logic course and research papers in stability theory. The book prepares the student for research in any of today's branches of stability theory, and gives an introduction to classification theory with an exposition of Morley's Categoricity Theorem.

Theory of Linear Models

Author: Bent Jorgensen

Publisher: CRC Press

ISBN: 9780412042614

Category: Mathematics

Page: 240

View: 5366

DOWNLOAD NOW »

This book provides a self-contained exposition of the theory of linear models, including practical aspects of residuals and data analysis.

Logic Colloquium '03

Lecture Notes in Logic 24

Author: Viggo Stoltenberg-Hansen,Jouko Väänänen

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 408

View: 4424

DOWNLOAD NOW »

This book is a compilation of papers resented at the 2003 European Summer Meeting of the Association for Symbolic Logic. It includes tutorials and research articles from some of the world's preeminent logicians. Of particular interest is a tutorial on finite model theory and query languages that lie between first-order and second-order logic. Other articles cover current research topics in all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, Computability Theory, and Philosophy.

Surveys in Set Theory

Author: A. R. D. Mathias

Publisher: Cambridge University Press

ISBN: 0521277337

Category: Mathematics

Page: 247

View: 6483

DOWNLOAD NOW »

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Vorlesungen Über die Zahlentheorie der Quaternionen

Author: Adolf Hurwitz

Publisher: Springer-Verlag

ISBN: 3642475361

Category: Mathematics

Page: 76

View: 7478

DOWNLOAD NOW »

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Turing's Legacy

Developments from Turing's Ideas in Logic

Author: Rod Downey

Publisher: Cambridge University Press

ISBN: 1107043484

Category: Computers

Page: 539

View: 1513

DOWNLOAD NOW »

A collection of essays celebrating the influence of Alan Turing's work in logic, computer science and related areas.

Applications of Model Theory to Functional Analysis

Author: Jose Iovino

Publisher: Courier Corporation

ISBN: 0486798615

Category: Mathematics

Page: 112

View: 7601

DOWNLOAD NOW »

The first self-contained introduction to techniques of model theory, this 2002 text presents material still not readily available elsewhere, including Krivine's theorem and the Krivine-Maurey theorem on stable Banach spaces.

A Course in Mathematical Logic

Author: John Lane Bell,Moshé Machover

Publisher: North-Holland

ISBN: N.A

Category: Computers

Page: 599

View: 8716

DOWNLOAD NOW »

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

Logic Colloquium 2005

Author: Costas Dimitracopoulos

Publisher: Cambridge University Press

ISBN: 052188425X

Category: Computers

Page: 272

View: 4452

DOWNLOAD NOW »

This 2007 volume includes surveys, tutorials, and selected research papers on advances in logic.

Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

Author: Guanrong Chen,Trung Tat Pham

Publisher: CRC Press

ISBN: 9781420039818

Category: Mathematics

Page: 328

View: 4404

DOWNLOAD NOW »

In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art" of building a working fuzzy controller has turned into today's "science" of systematic design. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. The authors proceed through basic fuzzy mathematics and fuzzy systems theory and conclude with an exploration of some industrial application examples. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. Mastering its contents gives students a clear understanding of fuzzy control systems theory that prepares them for deeper and broader studies and for many practical challenges faced in modern industry.

Descriptive Set Theory and Forcing

Author: Arnold W. Miller

Publisher: Cambridge University Press

ISBN: 1107168066

Category: Mathematics

Page: 134

View: 2414

DOWNLOAD NOW »

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the fourth publication in the Lecture Notes in Logic series, Miller develops the necessary features of the theory of descriptive sets in order to present a new proof of Louveau's separation theorem for analytic sets. While some background in mathematical logic and set theory is assumed, the material is based on a graduate course given by the author at the University of Wisconsin, Madison, and is thus accessible to students and researchers alike in these areas, as well as in mathematical analysis.