Model Theory An Introduction

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures This book is a ...

Author: David Marker

Publisher: Springer Science & Business Media

ISBN: 9780387227344

Category: Mathematics

Page: 345

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Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
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A Course in Model Theory

Translated from the French, this book is an introduction to first-order model theory.

Author: Bruno Poizat

Publisher: Springer Science & Business Media

ISBN: 9781441986221

Category: Mathematics

Page: 443

View: 101

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Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
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Introduction to Model Theory

So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory.

Author: Philipp Rothmaler

Publisher: CRC Press

ISBN: 9780429668500

Category: Mathematics

Page: 324

View: 274

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Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
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Model Theory

Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract ...

Author: C.C. Chang

Publisher: Elsevier

ISBN: 008088007X

Category: Computers

Page: 649

View: 174

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Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
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A Course in Model Theory

Concise introduction to current topics in model theory, including simple and stable theories.

Author: Katrin Tent

Publisher: Cambridge University Press

ISBN: 9780521763240

Category: Mathematics

Page: 248

View: 691

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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.
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A Shorter Model Theory

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory.

Author: Wilfrid Hodges

Publisher: Cambridge University Press

ISBN: 0521587131

Category: Mathematics

Page: 310

View: 578

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This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
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Mathematical Logic and Model Theory

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.

Author: Alexander Prestel

Publisher: Springer Science & Business Media

ISBN: 9781447121763

Category: Mathematics

Page: 194

View: 605

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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.
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Introduction to Mathematical Logic

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic.

Author: Jerome Malitz

Publisher: Springer Science & Business Media

ISBN: 9781461394419

Category: Mathematics

Page: 198

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This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.
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Model Theory and Algebraic Geometry

The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory.

Author: Elisabeth Bouscaren

Publisher: Springer

ISBN: 9783540685210

Category: Mathematics

Page: 216

View: 454

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This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
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Model Theory Algebra and Geometry

Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.

Author: Professor of Mathematics Anand Pillay

Publisher: Cambridge University Press

ISBN: 0521780683

Category: Mathematics

Page: 227

View: 921

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Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
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An Invitation to Model Theory

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

Author: Jonathan Kirby

Publisher: Cambridge University Press

ISBN: 9781107163881

Category: Mathematics

Page: 195

View: 269

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

In order to understand many of the proofs in this text the reader should have a one-semester background in set theory, including discussions of ordinal numbers, general a Cartesian products, cardinal arithmetic, and several forms of the ...

Author: Ralph Kopperman

Publisher:

ISBN: UOM:39015017282065

Category: Model theory

Page: 333

View: 837

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In order to understand many of the proofs in this text the reader should have a one-semester background in set theory, including discussions of ordinal numbers, general a Cartesian products, cardinal arithmetic, and several forms of the axiom choice.
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A First Course in Logic

Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course ...

Author: Shawn Hedman

Publisher: Oxford University Press on Demand

ISBN: 0198529813

Category: Mathematics

Page: 431

View: 531

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"The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, thistext covers the fundamental topics in classical logic in a clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, andmodel theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course."--BOOK JACKET.
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Lectures on Infinitary Model Theory

This book is the first modern introduction to the logic of infinitary languages in forty years, and is aimed at graduate students and researchers in all areas of mathematical logic.

Author: David Marker

Publisher: Cambridge University Press

ISBN: 9781107181939

Category: Mathematics

Page: 192

View: 321

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Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theory are provided, as is an appendix on admissible model theory.
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Model Theory for Beginners 15 Lectures

This book presents an introduction to model theory in 15 lectures.

Author: Roman Kossak

Publisher:

ISBN: 1848903618

Category:

Page: 152

View: 303

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This book presents an introduction to model theory in 15 lectures. It concentrates on several key concepts: first-order definability, classification of complete types, elementary extensions, categoricity, automorphisms, and saturation; all illustrated with examples that require neither advanced alegbra nor set theory. A full proof of the compactness theorem for countable languages and its applications are given, followed by a discussion of the Ehrefeucht-Mostowski technique for constructing models admitting automorphisms. Additional topics include recursive saturation, nonstandard models of arithmetic, Abraham Robinson's model-theoretic proof of Tarski's theorem on undefinability of truth, and the proof of the Infinite Ramsey Theorem using an elementary extension of the standard model of arithmetic.
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Model Theory and Modules

In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules.

Author: M. Prest

Publisher: Cambridge University Press

ISBN: 0521348331

Category: Mathematics

Page: 380

View: 696

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In recent years the interplay between model theory and other branches of mathematics has led to many deep and intriguing results. In this, the first book on the topic, the theme is the interplay between model theory and the theory of modules. The book is intended to be a self-contained introduction to the subject and introduces the requisite model theory and module theory as it is needed. Dr Prest develops the basic ideas concerning what can be said about modules using the information which may be expressed in a first-order language. Later chapters discuss stability-theoretic aspects of modules, and structure and classification theorems over various types of rings and for certain classes of modules. Both algebraists and logicians will enjoy this account of an area in which algebra and model theory interact in a significant way. The book includes numerous examples and exercises and consequently will make an ideal introduction for graduate students coming to this subject for the first time.
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