A Course in Model Theory

Author: Katrin Tent,Martin Ziegler

Publisher: Cambridge University Press

ISBN: 052176324X

Category: Mathematics

Page: 248

View: 499

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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

View: 6250

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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: 4084

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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 of stochastic processes

Author: Sergio Fajardo,H. Jerome Keisler

Publisher: A K Peters Ltd

ISBN: 9781568811673

Category: Mathematics

Page: 136

View: 1162

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This book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them.

An Introduction to Stability Theory

Author: Anand Pillay

Publisher: Courier Corporation

ISBN: 0486150437

Category: Mathematics

Page: 160

View: 3865

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This introductory treatment covers the basic concepts and machinery of stability theory. Full of examples, theorems, propositions, and problems, it is suitable for graduate students, professional mathematicians, and computer scientists. 1983 edition.

Mathematical Methods in Linguistics

Author: Barbara B.H. Partee,A.G. ter Meulen,R. Wall

Publisher: Springer Science & Business Media

ISBN: 9400922132

Category: Language Arts & Disciplines

Page: 666

View: 3255

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Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.

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: 2656

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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.

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: 7086

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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.

A Course in Mathematical Logic

Author: Yu.I. Manin

Publisher: Springer Science & Business Media

ISBN: 1475743858

Category: Mathematics

Page: 288

View: 8834

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1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.

A Guide to NIP Theories

Author: Pierre Simon

Publisher: Cambridge University Press

ISBN: 1107057752

Category: Mathematics

Page: 166

View: 1944

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The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.

Models and Games

Author: Jouko Väänänen

Publisher: Cambridge University Press

ISBN: 1139496336

Category: Mathematics

Page: N.A

View: 858

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This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.

A Course in Mathematical Logic

Author: John Lane Bell,Moshe Machover

Publisher: Elsevier

ISBN: 0080934749

Category: Logic, Symbolic and mathematical

Page: 599

View: 2336

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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.

Classical Descriptive Set Theory

Author: Alexander Kechris

Publisher: Springer Science & Business Media

ISBN: 1461241901

Category: Mathematics

Page: 404

View: 3760

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Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

A Course on Basic Model Theory

Author: Haimanti Sarbadhikari,Shashi Mohan Srivastava

Publisher: Springer

ISBN: 9811050988

Category: Mathematics

Page: 291

View: 9963

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This self-contained book is an exposition of the fundamental ideas of model theory. It presents the necessary background from logic, set theory and other topics of mathematics. Only some degree of mathematical maturity and willingness to assimilate ideas from diverse areas are required. The book can be used for both teaching and self-study, ideally over two semesters. It is primarily aimed at graduate students in mathematical logic who want to specialise in model theory. However, the first two chapters constitute the first introduction to the subject and can be covered in one-semester course to senior undergraduate students in mathematical logic. The book is also suitable for researchers who wish to use model theory in their work.

Notes On The Theory Of Choice

Author: David Kreps

Publisher: Routledge

ISBN: 0429978243

Category: Social Science

Page: 228

View: 2845

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In this book, Professor Kreps presents a first course on the basic models of choice theory that underlie much of economic theory. This course, taught for several years at the Graduate School of Business, Stanford University, gives the student an introduction to the axiomatic method of economic analysis, without placing too heavy a demand on mathematical sophistication.The course begins with the basics of choice and revealed preference theory and then discusses numerical representations of ordinal preference. Models with uncertainty come next: First is von Neumann?Morgenstern utility, and then choice under uncertainty with subjective uncertainty, using the formulation of Anscombe and Aumann, and then sketching the development of Savage's classic theory. Finally, the course delves into a number of special topics, including de Finetti's theorem, modeling choice on a part of a larger problem, dynamic choice, and the empirical evidence against the classic models.

An Introduction to Mathematical Logic and Type Theory

To Truth Through Proof

Author: Peter B. Andrews

Publisher: Springer Science & Business Media

ISBN: 9401599343

Category: Mathematics

Page: 390

View: 554

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In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Economic Fables

Author: Ariel Rubinstein

Publisher: Open Book Publishers

ISBN: 1906924775

Category: Biography & Autobiography

Page: 255

View: 1778

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"I had the good fortune to grow up in a wonderful area of Jerusalem, surrounded by a diverse range of people: Rabbi Meizel, the communist Sala Marcel, my widowed Aunt Hannah, and the intellectual Yaacovson. As far as I'm concerned, the opinion of such people is just as authoritative for making social and economic decisions as the opinion of an expert using a model." Part memoir, part crash-course in economic theory, this deeply engaging book by one of the world's foremost economists looks at economic ideas through a personal lens. Together with an introduction to some of the central concepts in modern economic thought, Ariel Rubinstein offers some powerful and entertaining reflections on his childhood, family and career. In doing so, he challenges many of the central tenets of game theory, and sheds light on the role economics can play in society at large. Economic Fables is as thought-provoking for seasoned economists as it is enlightening for newcomers to the field.

First Order Categorical Logic

Model-Theoretical Methods in the Theory of Topoi and Related Categories

Author: M. Makkai,G.E. Reyes

Publisher: Springer

ISBN: 3540371001

Category: Mathematics

Page: 318

View: 9104

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