A Course in Model Theory

Author: Katrin Tent,Martin Ziegler

Publisher: Cambridge University Press

ISBN: 052176324X

Category: Mathematics

Page: 248

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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

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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.

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: 669

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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.

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: 1491

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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.

An Invitation to Model Theory

Author: Jonathan Kirby

Publisher: Cambridge University Press

ISBN: 1107163889

Category: Mathematics

Page: 195

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An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.

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

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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.

Theory of Linear Models

Author: Bent Jorgensen

Publisher: CRC Press

ISBN: 9780412042614

Category: Mathematics

Page: 240

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

Turing's Legacy

Developments from Turing's Ideas in Logic

Author: Rod Downey

Publisher: Cambridge University Press

ISBN: 1107043484

Category: Computers

Page: 539

View: 843

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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

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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.

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: 7021

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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.

Logic Colloquium 2005

Author: Costas Dimitracopoulos,Ludomir Newelski,Dag Normann,John R. Steel

Publisher: Cambridge University Press

ISBN: 1139467255

Category: Mathematics

Page: 272

View: 3351

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The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

A Course in Mathematical Logic

Author: John Lane Bell,Moshé Machover

Publisher: North-Holland

ISBN: N.A

Category: Computers

Page: 599

View: 1851

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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.

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

Author: George Tourlakis

Publisher: Cambridge University Press

ISBN: 9781139439435

Category: Mathematics

Page: N.A

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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.

Logic in Tehran

proceedings of the Workshop and Conference on Logic, Algebra and Arithmetic, held October 18-22, 2003

Author: Ali Enayat,Iraj Kalantari,Mojtaba Moniri

Publisher: A K Peters Ltd

ISBN: 9781568812953

Category: Mathematics

Page: 341

View: 6291

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This collection of papers is based on a conference that was held in Tehran, Iran, with the express purpose of bringing together researchers with connections to Iranian logicians and promoting further research in mathematical logic in Iran. Particular emphasis was given to model theory and its applications to algebra and formal theories of arithmetic. Other papers address category theory, computability, modal logic, and the history of mathematical logic in Iran.

Logik, Wissenschaftstheorie und Erkenntnistheorie

Akten des 11. Internationalen Wittgenstein Symposiums, 4. bis 13. August 1986, Kirchberg am Wechsel (Österreich) : ausgewählte Beiträge

Author: Paul Weingartner,Gerhard Schurz

Publisher: Holder Pichler Tempsky

ISBN: N.A

Category: Philosophy

Page: 430

View: 3138

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Logic Colloquium '85

proceedings of the colloquium held in Orsay, France, July 1985

Author: Equipe de logique mathématique (Paris, France)

Publisher: North Holland

ISBN: 9780444702111

Category: Mathematics

Page: 308

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The bulk of this volume consists of invited addresses presented at the Colloquium. These contributions report on recent or ongoing research in some of the mainstream areas of mathematical logic: model theory, both pure and in its applications (to group theory and real algebraic geometry); and proof theory, applied to set theory and diophantine equations. The major novel aspect of the book is the important place accorded to the connections of mathematical logic with the neighboring disciplines: mathematical foundations of computer science, and philosophy of mathematics.

Models of Peano arithmetic

Author: Richard Kaye

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Literary Criticism

Page: 292

View: 6398

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Non-standard models of arithmetic are of interest to mathematicians through the presence of infinite integers and the various properties they inherit from the finite integers. Since their introduction in the 1930s, they have come to play an important role in model theory, and in combinatorics through independence results such as the Paris-Harrington theorem. This book is an introduction to these developments, and stresses the interplay between the first-order theory, recursion-theoretic aspects, and the structural properties of these models. Prerequisites for an understanding of the text have been kept to a minimum, these being a basic grounding in elementary model theory and a familiarity with the notions of recursive, primitive recursive, and r.e. sets. Consequently, the book is suitable for postgraduate students coming to the subject for the first time, and a number of exercises of varying degrees of difficulty will help to further the reader's understanding.

Lectures on Hyperbolic Geometry

Author: Riccardo Benedetti,Carlo Petronio

Publisher: Springer Science & Business Media

ISBN: 9783540555346

Category: Mathematics

Page: 330

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The core of the book is the study of the space of the hyperbolic manifolds endowed with the Chabauty and the geometric topology, and in particular the proof of the hypberbolic surgery theorem in dimension three, based on the representation of three-mainfolds as glued ideal tetrahedra. The development of this main theme requires setting a wide background forming the body of the book: the classical geometry of the hyperbolic space, the Fenchel-Nielsen parametrization of the Teichmüller space, Mostow's rigidity theorem, Margulis' lemma. As a conclusion some features of bounded cohomology, flat fiber bundles and amenable groups are mentioned.