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Model Theory In Algebra Analysis And Arithmetic

Author : Lou van den Dries
ISBN : 9783642549366
Genre : Mathematics
File Size : 30. 1 MB
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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.

Model Theory Of Algebra And Arithmetic

Author : L. Pacholski
ISBN : 9783540383932
Genre : Mathematics
File Size : 29. 24 MB
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Model Theory

Author : C.C. Chang
ISBN : 008088007X
Genre : Computers
File Size : 35. 79 MB
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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.

Model Theory Of Algebra And Arithmetic

Author : L. Pacholski
ISBN : 3662187930
Genre :
File Size : 73. 86 MB
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Building Models By Games

Author : Wilfrid Hodges
ISBN : 0521317169
Genre : Mathematics
File Size : 35. 45 MB
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This book introduces a general method for building infinite mathematical structures, and surveys its applications in algebra and model theory. The basic idea behind the method is to build a structure by a procedure with infinitely many steps, similar to a game between two players that goes on indefinitely. The approach is new and helps to simplify, motivate and unify a wide range of constructions that were previously carried out separately and by ad hoc methods. The first chapter provides a resume of basic model theory. A wide variety of algebraic applications are studied, with detailed analyses of existentially closed groups of class 2. Another chapter describes the classical model-theoretic form of this method -of construction, which is known variously as 'omitting types', 'forcing' or the 'Henkin-Orey theorem'. The last three chapters are more specialised and discuss how the same idea can be used to build uncountable structures. Applications include completeness for Magidor-Malitz quantifiers, and Shelah's recent and sophisticated omitting types theorem for L(Q). There are also applications to Bdolean algebras and models of arithmetic.

Model Theory

Author : María Manzano
ISBN : 0198538510
Genre : Computers
File Size : 44. 6 MB
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Model theory is the branch of mathematical logic looking at the relationship between mathematical structures and logic languages. These formal languages are free from the ambiguities of natural languages, and are becoming increasingly important in areas such as computing, philosophy and linguistics. This book provides a clear introduction to the subject for both mathematicians and the non-specialists now needing to learn some model theory.

Connections Between Model Theory And Algebraic And Analytic Geometry

Author : Angus Macintyre
ISBN : UOM:39015056471173
Genre : Mathematics
File Size : 51. 2 MB
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Logic In Tehran

Author : Ali Enayat
ISBN : 9781108670005
Genre : Mathematics
File Size : 32. 78 MB
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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. This volume, the twenty-sixth publication in the Lecture Notes in Logic series, contains the proceedings of the 'Workshop and Conference on Logic, Algebra and Arithmetic' held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran, Iran in October, 2003. These papers are mostly revised and expanded versions of those that were originally presented at the meeting and address all areas of mathematical logic. The book also includes a short history of mathematical logic in Iran.

Building Models By Games

Author : Wilfrid Hodges
ISBN : 9780486450179
Genre : Mathematics
File Size : 78. 83 MB
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This volume introduces a general method for building infinite mathematical structures and surveys applications in algebra and model theory. It covers basic model theory and examines a variety of algebraic applications, including completeness for Magidor-Malitz quantifiers, Shelah's recent and sophisticated omitting types theorem for L(Q), and applications to Boolean algebras. Over 160 exercises. 1985 edition.

Model Theoretic Algebra With Particular Emphasis On Fields Rings Modules

Author : Christian.U Jensen
ISBN : 9781351431125
Genre : Mathematics
File Size : 73. 1 MB
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This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.

Recursion Theory Week

Author : Heinz-Dieter Ebbinghaus
ISBN : 9783540395966
Genre : Mathematics
File Size : 28. 46 MB
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The Use Of Ultraproducts In Commutative Algebra

Author : Hans Schoutens
ISBN : 9783642133671
Genre : Mathematics
File Size : 88. 94 MB
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Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.

Logic Colloquium 85

Author : The Paris Logic Group
ISBN : 9780444535825
Genre : Mathematics
File Size : 71. 22 MB
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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.

Model Theory An Introduction

Author : David Marker
ISBN : 9780387227344
Genre : Mathematics
File Size : 24. 31 MB
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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

The Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournaments

Author : Gregory L. Cherlin
ISBN : 0821808362
Genre : Mathematics
File Size : 58. 41 MB
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In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use. Features: Interface between combinatorics and model theory Unusual use of Ramsey's theorem to classify structures An extension of an already elaborate branch of model theory The first monograph on Lachlan's method

Model Theory Of Algebra And Arithmetic

Author : Leszek Pacholski
ISBN : OCLC:654510856
Genre : Algebra
File Size : 55. 35 MB
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Groups Modules And Model Theory Surveys And Recent Developments

Author : Manfred Droste
ISBN : 9783319517186
Genre : Mathematics
File Size : 32. 43 MB
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This volume focuses on group theory and model theory with a particular emphasis on the interplay of the two areas. The survey papers provide an overview of the developments across group, module, and model theory while the research papers present the most recent study in those same areas. With introductory sections that make the topics easily accessible to students, the papers in this volume will appeal to beginning graduate students and experienced researchers alike. As a whole, this book offers a cross-section view of the areas in group, module, and model theory, covering topics such as DP-minimal groups, Abelian groups, countable 1-transitive trees, and module approximations. The papers in this book are the proceedings of the conference “New Pathways between Group Theory and Model Theory,” which took place February 1-4, 2016, in Mülheim an der Ruhr, Germany, in honor of the editors’ colleague Rüdiger Göbel. This publication is dedicated to Professor Göbel, who passed away in 2014. He was one of the leading experts in Abelian group theory.

Algebraic K Theory Evanston 1980

Author : Eric Friedlander
ISBN : 9783540386469
Genre : Mathematics
File Size : 82. 19 MB
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Model Theoretic Logics

Author : J. Barwise
ISBN : 9781316739396
Genre : Mathematics
File Size : 40. 27 MB
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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. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.

A Course In Model Theory

Author : Bruno Poizat
ISBN : 9781441986221
Genre : Mathematics
File Size : 71. 61 MB
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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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